#' -----------------------------------------------------------------------------
#' Install the new version of the package
#' -----------------------------------------------------------------------------

#library(devtools)
#install_github("lvhoskovec/mmpack", build_vignettes = TRUE, force = TRUE)

library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──
## ✓ ggplot2 3.3.2     ✓ purrr   0.3.4
## ✓ tibble  3.0.4     ✓ dplyr   1.0.2
## ✓ tidyr   1.1.2     ✓ stringr 1.4.0
## ✓ readr   1.3.1     ✓ forcats 0.5.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library(lubridate)
## 
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union
library(haven)
library(readxl)
library(mmpack)

#' For ggplots
simple_theme <- theme(
  #aspect.ratio = 1,
  text  = element_text(family="Calibri",size = 12, color = 'black'),
  panel.spacing.y = unit(0,"cm"),
  panel.spacing.x = unit(0.25, "lines"),
  panel.grid.minor = element_line(color = "transparent"),
  panel.grid.major = element_line(color = "transparent"),
  panel.border=element_rect(fill = NA),
  panel.background=element_blank(),
  axis.ticks = element_line(colour = "black"),
  axis.text = element_text(color = "black", size=10),
  # legend.position = c(0.1,0.1),
  plot.margin=grid::unit(c(0,0,0,0), "mm"),
  legend.key = element_blank()
)
# windowsFonts(Calibri=windowsFont("TT Calibri"))
options(scipen = 9999) #avoid scientific notation

In this version of the analysis, we wanted to try a few things to refine our model and check some things out. After meeting with Ander, Lauren, and Sheryl, here’s what we’ve come up with:

  • The effect of ozone seen in the previous version of the model might actually be a seasonal signal. I’m going to add indicator variables for season of conception
  • Residual spatial confounding is also an issue given the spatial patterns in both the environmental (esp. ozone) and social exposures. We’re addressing this in two ways:
    • First, we’re adding lon, lat, and lon*lat to the covariates matrix
    • Second, we’re adding census tract percent POC (Total Pop - NHW / Total Pop * 100) to the exposures
  • In order to better compare the RIDGE and NPB models, I’m generating rescaled estimates and 95% CIs for the RIDGE coefficients

We also wanted to try rerunning the BKMR model with exposures selected by the NPB model. If we have 3 predictors with a PIP > 0.5 (or close to it), we can include them in a BKMR. Alternatively, for 1-2 exposures, we can just look at a GAM

Lauren is going to add a frame to the summary() function that will give us posterior means and CIs for the covariates (but they won’t have PIPs)

1 Exploring the data set

The HS data set was previously used in the CEI paper (Martenies et al., 2019). In the original analysis, we used an exposure index based on the CalEnvironScreen tool. We observed lower birth weights and lower adiposity associated with higher index scores, driven largely by exposures to social indicators of health at the neighborhood level. Now, we are aiming to use methods for mixtures to try to identify which exposures are driving these association.

The complete data set for the birth weight outcome consists of n = 897 participants. This represents 77.93% of the original Healthy Start 1 cohort.

Of the 897 participants, 27% identify as Latina, 17% identify as Black, and 27% identify as another non-NHW race or ethnicity. The median age of mothers in this dataset is 28 years. 51% of babies born were male.

1.1 Effect of year on birth weight

In models below, Ander noticed an effect of year of conception on birth weight. Conception year was included in models below as dummy variables. I’m not sure why this effect exists. Here I am plotting birth weight against date of birth. The trend line ever so slighly increases over time.

plot(hs_data1$dob, hs_data1$birth_weight)
abline(lm(birth_weight ~ dob, data = hs_data1), col = "red")

Grouping birth weights by conception year doesn’t show much of a trend:

bw_trends_by_concept <- ggplot(data = hs_data1) +
  geom_boxplot(aes(x = concep_year, group = concep_year, y = birth_weight))
bw_trends_by_concept
## Warning: Removed 5 rows containing non-finite values (stat_boxplot).

1.2 Exposure data

We have included 19 exposures in our analysis.

These exposures are based on the census tract where each mother lived at the time of enrollment into Healthy Start. With the exception of air pollution (mean_pm and mean_o3), these are based on long-term averages at for each census tract. For mean_pm and mean_o3 are based on the average pollution levels across each pregnancy (est. conception date to delivery date) estimated using ordinary kriging and monitoring data.

#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, pct_tree_cover, pct_impervious,
            mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
            cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
            pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
  as.matrix()
head(X)
##       mean_pm  mean_o3 pct_tree_cover pct_impervious mean_aadt_intensity
## [1,] 8.483046 47.19072       6.006276       43.30893          10128.4962
## [2,] 6.598608 50.05090       7.281109       48.36432          10749.0359
## [3,] 7.454146 48.57052      17.205991       31.67281           9048.6468
## [4,] 6.671239 50.06429       6.842898       45.00359           4223.3434
## [5,] 7.122537 50.14275       3.357792       28.16745            858.7283
## [6,] 7.637453 47.03125      10.743612       45.87564          15603.9800
##      dist_m_tri dist_m_npl dist_m_waste_site dist_m_major_emit dist_m_cafo
## [1,]   2827.538   729.2371          4829.780          7968.654    29116.58
## [2,]   1576.420  5239.2211          4417.792          3780.951    51044.30
## [3,]   3350.303  2992.2968          5211.871          7423.232    36079.21
## [4,]   3364.954  6998.1286          8921.318          9636.816    42235.78
## [5,]   2923.811  3427.2247          7006.042          6806.912    29145.98
## [6,]   3364.200  3166.5395          4484.960          5265.285    43921.85
##      dist_m_mine_well cvd_rate_adj res_rate_adj violent_crime_rate
## [1,]        1749.1256     275.2480     155.7767          14.377133
## [2,]        7354.5310     279.6435     226.8038           8.905404
## [3,]        4887.2996     221.0414     157.6974           7.636888
## [4,]        3752.6399     203.8812     142.5368           2.850212
## [5,]         729.7784     194.1983     101.0046           5.435988
## [6,]        5870.6867     174.3361     120.3281           5.035971
##      property_crime_rate pct_less_hs pct_unemp pct_limited_eng pct_hh_pov
## [1,]            37.32935   31.784946 11.529628       26.114650  12.010919
## [2,]            67.03932   15.290231  4.908306        8.500401  18.123496
## [3,]            46.78194    6.891702  4.564963        0.000000   6.307978
## [4,]            21.95270    2.725915  5.623583        1.350621   9.292274
## [5,]            22.49834   12.919186  5.234103        6.307385   2.115768
## [6,]            47.15500    3.842365 10.000000        5.121799  25.171768
##       pct_poc
## [1,] 90.33703
## [2,] 30.44025
## [3,] 26.63305
## [4,] 32.68648
## [5,] 73.60772
## [6,] 23.08698

Variance and histograms of the exposure variables (in their original units):

var(X)
##                             mean_pm        mean_o3 pct_tree_cover
## mean_pm                 0.391784015    0.006083605     -0.2054297
## mean_o3                 0.006083605    9.383489039     -0.4158151
## pct_tree_cover         -0.205429726   -0.415815089      9.7193077
## pct_impervious          0.508898445   -1.674151031      5.8719893
## mean_aadt_intensity  -182.234953786  474.627052967   8431.6446632
## dist_m_tri           -255.176839682  444.286548683    -73.1423054
## dist_m_npl           -289.002141382  539.849185829    434.4654007
## dist_m_waste_site    -275.262105884  261.902915064   1933.8647304
## dist_m_major_emit      71.096593638  577.257325397    265.4284518
## dist_m_cafo         -1291.237441927  -35.275020052  10170.6234275
## dist_m_mine_well     -339.250592215 -375.434990683   3136.3680766
## cvd_rate_adj            3.871688575    0.939328342    -24.8232924
## res_rate_adj            2.356328835   -0.181515705     -3.5331376
## violent_crime_rate      0.232839920    0.577648302     -4.0583754
## property_crime_rate     2.001989749   -2.773092354    -22.6429724
## pct_less_hs             1.132232861    0.637361326     -7.5753471
## pct_unemp               0.100439902    0.288530482     -0.3330523
## pct_limited_eng         0.432516169    0.295617023     -2.8349116
## pct_hh_pov              0.731824476   -0.606648513      0.3805472
## pct_poc                 1.632059580    1.202932299    -19.4091792
##                     pct_impervious mean_aadt_intensity     dist_m_tri
## mean_pm                  0.5088984           -182.2350     -255.17684
## mean_o3                 -1.6741510            474.6271      444.28655
## pct_tree_cover           5.8719893           8431.6447      -73.14231
## pct_impervious         176.8316214          55459.6063   -15279.44024
## mean_aadt_intensity  55459.6063235       67283287.0201 -1315386.69307
## dist_m_tri          -15279.4402428       -1315386.6931  6558190.20296
## dist_m_npl           -7729.3843793        1683196.0799  4282727.94125
## dist_m_waste_site    -4662.9983638        2039577.9230  2441267.84540
## dist_m_major_emit     2627.0270993        2477155.3406  1433153.16531
## dist_m_cafo          16586.9964129       15462371.9832  3431065.70215
## dist_m_mine_well       706.6674650        2073244.5987   995872.11873
## cvd_rate_adj           230.4542985          20477.4374   -49347.60273
## res_rate_adj           176.8108084          33055.3733   -31870.98664
## violent_crime_rate      26.6945028           5736.5627    -1014.08753
## property_crime_rate    118.0737725          22077.3894    -5365.69285
## pct_less_hs             56.8383947          -4056.6889   -12372.14262
## pct_unemp               25.9434246           6003.3343    -2527.22451
## pct_limited_eng         41.9919053           2620.6198    -5408.86434
## pct_hh_pov              82.2198624          17850.1649    -8842.76408
## pct_poc                 88.3560154           4526.2710   -18049.42332
##                        dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm                 -289.0021         -275.2621          71.09659
## mean_o3                  539.8492          261.9029         577.25733
## pct_tree_cover           434.4654         1933.8647         265.42845
## pct_impervious         -7729.3844        -4662.9984        2627.02710
## mean_aadt_intensity  1683196.0799      2039577.9230     2477155.34057
## dist_m_tri           4282727.9413      2441267.8454     1433153.16531
## dist_m_npl          11125411.7474      4193498.0586     6948817.25739
## dist_m_waste_site    4193498.0586      5344101.7540     1395277.06805
## dist_m_major_emit    6948817.2574      1395277.0681    10114549.72263
## dist_m_cafo          5416531.1320      5586018.8251    -2993791.05377
## dist_m_mine_well      256924.3029      1375784.7856    -1810174.74785
## cvd_rate_adj          -30921.0390       -43119.5785       16272.40152
## res_rate_adj          -19393.1304       -32402.8440       -1320.21297
## violent_crime_rate      -672.9264        -3702.6112        -360.49700
## property_crime_rate   -18283.4264       -22350.3006      -24007.42305
## pct_less_hs            -6760.5337       -11422.4985        8866.74917
## pct_unemp               2195.0515        -1476.4094        5212.74830
## pct_limited_eng          498.0033        -4277.8134        9367.28435
## pct_hh_pov             -1135.3843        -7599.7432        8682.26135
## pct_poc                -1456.8941        -8602.8521       22698.24353
##                        dist_m_cafo dist_m_mine_well   cvd_rate_adj
## mean_pm                -1291.23744        -339.2506      3.8716886
## mean_o3                  -35.27502        -375.4350      0.9393283
## pct_tree_cover         10170.62343        3136.3681    -24.8232924
## pct_impervious         16586.99641         706.6675    230.4542985
## mean_aadt_intensity 15462371.98316     2073244.5987  20477.4373759
## dist_m_tri           3431065.70215      995872.1187 -49347.6027339
## dist_m_npl           5416531.13199      256924.3029 -30921.0389720
## dist_m_waste_site    5586018.82514     1375784.7856 -43119.5785165
## dist_m_major_emit   -2993791.05377    -1810174.7478  16272.4015197
## dist_m_cafo         46324000.89481     9345575.3772 -46645.9665229
## dist_m_mine_well     9345575.37722     4430024.9964 -39046.5984701
## cvd_rate_adj          -46645.96652      -39046.5985   2039.8569530
## res_rate_adj          -13772.40263      -16322.5110   1289.5661935
## violent_crime_rate       722.31907       -2032.3464    135.9487143
## property_crime_rate   -15833.92381       -4272.3829    343.9364726
## pct_less_hs           -26060.83378      -10037.6577    328.3044447
## pct_unemp              -1030.96916       -2827.2369    105.0153846
## pct_limited_eng        -7089.15821       -4814.6687    183.5853966
## pct_hh_pov              -855.38016       -5030.4055    266.1004715
## pct_poc               -44526.37107      -24974.3303    618.2817294
##                       res_rate_adj violent_crime_rate property_crime_rate
## mean_pm                  2.3563288          0.2328399            2.001990
## mean_o3                 -0.1815157          0.5776483           -2.773092
## pct_tree_cover          -3.5331376         -4.0583754          -22.642972
## pct_impervious         176.8108084         26.6945028          118.073773
## mean_aadt_intensity  33055.3733277       5736.5627383        22077.389365
## dist_m_tri          -31870.9866403      -1014.0875345        -5365.692846
## dist_m_npl          -19393.1304345       -672.9263612       -18283.426420
## dist_m_waste_site   -32402.8439544      -3702.6111771       -22350.300554
## dist_m_major_emit    -1320.2129699       -360.4970006       -24007.423046
## dist_m_cafo         -13772.4026269        722.3190727       -15833.923813
## dist_m_mine_well    -16322.5110008      -2032.3464340        -4272.382880
## cvd_rate_adj          1289.5661935        135.9487143          343.936473
## res_rate_adj          1091.1856742        104.4979610          333.780710
## violent_crime_rate     104.4979610         40.1175363          160.725724
## property_crime_rate    333.7807097        160.7257236         1295.004010
## pct_less_hs            197.8827546         22.5579950           -3.138375
## pct_unemp               72.3576933         11.3130282            1.362247
## pct_limited_eng        104.0524036         12.7978322          -14.963510
## pct_hh_pov             201.6582659         29.1947400           64.236239
## pct_poc                297.8399442         46.4013012          -44.321973
##                        pct_less_hs     pct_unemp pct_limited_eng    pct_hh_pov
## mean_pm                  1.1322329     0.1004399       0.4325162     0.7318245
## mean_o3                  0.6373613     0.2885305       0.2956170    -0.6066485
## pct_tree_cover          -7.5753471    -0.3330523      -2.8349116     0.3805472
## pct_impervious          56.8383947    25.9434246      41.9919053    82.2198624
## mean_aadt_intensity  -4056.6889048  6003.3343312    2620.6197529 17850.1649192
## dist_m_tri          -12372.1426191 -2527.2245090   -5408.8643368 -8842.7640785
## dist_m_npl           -6760.5337115  2195.0514738     498.0033420 -1135.3843390
## dist_m_waste_site   -11422.4985495 -1476.4094188   -4277.8133935 -7599.7432386
## dist_m_major_emit     8866.7491706  5212.7483023    9367.2843472  8682.2613524
## dist_m_cafo         -26060.8337755 -1030.9691591   -7089.1582114  -855.3801591
## dist_m_mine_well    -10037.6576614 -2827.2368665   -4814.6687400 -5030.4055237
## cvd_rate_adj           328.3044447   105.0153846     183.5853966   266.1004715
## res_rate_adj           197.8827546    72.3576933     104.0524036   201.6582659
## violent_crime_rate      22.5579950    11.3130282      12.7978322    29.1947400
## property_crime_rate     -3.1383751     1.3622468     -14.9635105    64.2362387
## pct_less_hs            162.1681017    39.4206217      85.1910014   100.9072175
## pct_unemp               39.4206217    24.6546969      25.2172769    36.9693212
## pct_limited_eng         85.1910014    25.2172769      68.6532943    67.2758215
## pct_hh_pov             100.9072175    36.9693212      67.2758215   119.7157808
## pct_poc                238.8801445    72.7999599     142.1961838   155.4992975
##                           pct_poc
## mean_pm                  1.632060
## mean_o3                  1.202932
## pct_tree_cover         -19.409179
## pct_impervious          88.356015
## mean_aadt_intensity   4526.271046
## dist_m_tri          -18049.423325
## dist_m_npl           -1456.894145
## dist_m_waste_site    -8602.852068
## dist_m_major_emit    22698.243529
## dist_m_cafo         -44526.371072
## dist_m_mine_well    -24974.330302
## cvd_rate_adj           618.281729
## res_rate_adj           297.839944
## violent_crime_rate      46.401301
## property_crime_rate    -44.321973
## pct_less_hs            238.880145
## pct_unemp               72.799960
## pct_limited_eng        142.196184
## pct_hh_pov             155.499297
## pct_poc                524.759104
ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Scaling the exposure variables

X.scaled <- apply(X, 2, scale)
head(X.scaled)
##          mean_pm    mean_o3 pct_tree_cover pct_impervious mean_aadt_intensity
## [1,]  1.60876944 -0.2502907    -0.08261827      0.2084897         -0.02626143
## [2,] -1.40186806  0.6834152     0.32629926      0.5886571          0.04938980
## [3,] -0.03503482  0.2001460     3.50981981     -0.6665506         -0.15790801
## [4,] -1.28583023  0.6877893     0.18573791      0.3359288         -0.74617032
## [5,] -0.56482237  0.7133998    -0.93215008     -0.9301550         -1.15635722
## [6,]  0.25782234 -0.3023500     1.43693690      0.4015075          0.64126566
##      dist_m_tri  dist_m_npl dist_m_waste_site dist_m_major_emit dist_m_cafo
## [1,] -0.4008664 -1.44212141      -0.172775897        -0.1090638  -1.1354079
## [2,] -0.8894134 -0.08999604      -0.350992130        -1.4258114   2.0863310
## [3,] -0.1967327 -0.76363997      -0.007492447        -0.2805619  -0.1124210
## [4,] -0.1910117  0.43733697       1.597126043         0.4154599   0.7921355
## [5,] -0.3632728 -0.63324550       0.768623456        -0.4743524  -1.1310891
## [6,] -0.1913062 -0.71140077      -0.321936759        -0.9590895   1.0398621
##      dist_m_mine_well cvd_rate_adj res_rate_adj violent_crime_rate
## [1,]       -0.7748959    0.6917151   -0.2847192          0.2444833
## [2,]        1.8883051    0.7890362    1.8654606         -0.6194047
## [3,]        0.7160914   -0.5084805   -0.2265752         -0.8196807
## [4,]        0.1769998   -0.8884275   -0.6855261         -1.5754111
## [5,]       -1.2592010   -1.1028189   -1.9428184         -1.1671633
## [6,]        1.1833114   -1.5425892   -1.3578439         -1.2303189
##      property_crime_rate pct_less_hs   pct_unemp pct_limited_eng pct_hh_pov
## [1,]          -0.5008789  1.20091488  0.36793456      2.15383825 -0.3020187
## [2,]           0.3247153 -0.09436047 -0.96557105      0.02798425  0.2566428
## [3,]          -0.2382061 -0.75386917 -1.03471894     -0.99792447 -0.8232412
## [4,]          -0.9281724 -1.08099463 -0.82151747     -0.83491873 -0.5504902
## [5,]          -0.9130100 -0.28055077 -0.89995692     -0.23668961 -1.2063898
## [6,]          -0.2278392 -0.99332353  0.05987409     -0.37977738  0.9008223
##         pct_poc
## [1,]  1.5727240
## [2,] -1.0419857
## [3,] -1.2081839
## [4,] -0.9439299
## [5,]  0.8424295
## [6,] -1.3629822

Variance and histograms of the exposure variables (scaled):

var(X.scaled)
##                          mean_pm      mean_o3 pct_tree_cover pct_impervious
## mean_pm              1.000000000  0.003172893   -0.105274276     0.06114033
## mean_o3              0.003172893  1.000000000   -0.043541201    -0.04109912
## pct_tree_cover      -0.105274276 -0.043541201    1.000000000     0.14164056
## pct_impervious       0.061140333 -0.041099117    0.141640558     1.00000000
## mean_aadt_intensity -0.035493982  0.018889337    0.329716765     0.50844411
## dist_m_tri          -0.159193706  0.056635532   -0.009161339    -0.44867872
## dist_m_npl          -0.138426634  0.052836279    0.041781063    -0.17426369
## dist_m_waste_site   -0.190232937  0.036984589    0.268331135    -0.15168685
## dist_m_major_emit    0.035715124  0.059253499    0.026770503     0.06211712
## dist_m_cafo         -0.303095664 -0.001691929    0.479321466     0.18326720
## dist_m_mine_well    -0.257510042 -0.058230361    0.477976199     0.02524829
## cvd_rate_adj         0.136954783  0.006789463   -0.176295758     0.38371166
## res_rate_adj         0.113962827 -0.001793836   -0.034307854     0.40251263
## violent_crime_rate   0.058730941  0.029772424   -0.205526308     0.31693831
## property_crime_rate  0.088879773 -0.025156291   -0.201827442     0.24673907
## pct_less_hs          0.142046220  0.016338825   -0.190810449     0.33564418
## pct_unemp            0.032317153  0.018969666   -0.021515177     0.39291400
## pct_limited_eng      0.083396591  0.011647067   -0.109746623     0.38111402
## pct_hh_pov           0.106858205 -0.018100029    0.011156172     0.56509450
## pct_poc              0.113823690  0.017142692   -0.271775006     0.29005220
##                     mean_aadt_intensity   dist_m_tri  dist_m_npl
## mean_pm                     -0.03549398 -0.159193706 -0.13842663
## mean_o3                      0.01888934  0.056635532  0.05283628
## pct_tree_cover               0.32971677 -0.009161339  0.04178106
## pct_impervious               0.50844411 -0.448678724 -0.17426369
## mean_aadt_intensity          1.00000000 -0.062619247  0.06152095
## dist_m_tri                  -0.06261925  1.000000000  0.50138396
## dist_m_npl                   0.06152095  0.501383960  1.00000000
## dist_m_waste_site            0.10755964  0.412369055  0.54385239
## dist_m_major_emit            0.09495686  0.175965418  0.65505772
## dist_m_cafo                  0.27696155  0.196849357  0.23859436
## dist_m_mine_well             0.12008641  0.184760224  0.03659688
## cvd_rate_adj                 0.05527416 -0.426652406 -0.20525615
## res_rate_adj                 0.12199419 -0.376750794 -0.17601130
## violent_crime_rate           0.11041575 -0.062519618 -0.03185242
## property_crime_rate          0.07479259 -0.058223492 -0.15232247
## pct_less_hs                 -0.03883608 -0.379376300 -0.15916230
## pct_unemp                    0.14739715 -0.198747643  0.13253691
## pct_limited_eng              0.03855846 -0.254907958  0.01801953
## pct_hh_pov                   0.19888999 -0.315587892 -0.03111065
## pct_poc                      0.02408835 -0.307674381 -0.01906733
##                     dist_m_waste_site dist_m_major_emit  dist_m_cafo
## mean_pm                   -0.19023294        0.03571512 -0.303095664
## mean_o3                    0.03698459        0.05925350 -0.001691929
## pct_tree_cover             0.26833114        0.02677050  0.479321466
## pct_impervious            -0.15168685        0.06211712  0.183267205
## mean_aadt_intensity        0.10755964        0.09495686  0.276961553
## dist_m_tri                 0.41236906        0.17596542  0.196849357
## dist_m_npl                 0.54385239        0.65505772  0.238594356
## dist_m_waste_site          1.00000000        0.18977973  0.355027509
## dist_m_major_emit          0.18977973        1.00000000 -0.138307324
## dist_m_cafo                0.35502751       -0.13830732  1.000000000
## dist_m_mine_well           0.28275484       -0.27042332  0.652378929
## cvd_rate_adj              -0.41298787        0.11328659 -0.151743889
## res_rate_adj              -0.42432287       -0.01256670 -0.061257230
## violent_crime_rate        -0.25287368       -0.01789622  0.016755559
## property_crime_rate       -0.26866460       -0.20976678 -0.064647236
## pct_less_hs               -0.38800832        0.21893159 -0.300678627
## pct_unemp                 -0.12862329        0.33009857 -0.030506530
## pct_limited_eng           -0.22333346        0.35547555 -0.125707430
## pct_hh_pov                -0.30045944        0.24950766 -0.011486308
## pct_poc                   -0.16245202        0.31155805 -0.285584268
##                     dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm                  -0.25751004  0.136954783  0.113962827
## mean_o3                  -0.05823036  0.006789463 -0.001793836
## pct_tree_cover            0.47797620 -0.176295758 -0.034307854
## pct_impervious            0.02524829  0.383711656  0.402512635
## mean_aadt_intensity       0.12008641  0.055274160  0.121994187
## dist_m_tri                0.18476022 -0.426652406 -0.376750794
## dist_m_npl                0.03659688 -0.205256148 -0.176011297
## dist_m_waste_site         0.28275484 -0.412987865 -0.424322872
## dist_m_major_emit        -0.27042332  0.113286594 -0.012566704
## dist_m_cafo               0.65237893 -0.151743889 -0.061257230
## dist_m_mine_well          1.00000000 -0.410752544 -0.234765650
## cvd_rate_adj             -0.41075254  1.000000000  0.864359590
## res_rate_adj             -0.23476565  0.864359590  1.000000000
## violent_crime_rate       -0.15245003  0.475234675  0.499449246
## property_crime_rate      -0.05640681  0.211613232  0.280786581
## pct_less_hs              -0.37449548  0.570813439  0.470409304
## pct_unemp                -0.27052616  0.468277441  0.441149256
## pct_limited_eng          -0.27607853  0.490577454  0.380164971
## pct_hh_pov               -0.21843600  0.538480631  0.557944498
## pct_poc                  -0.51797735  0.597594464  0.393598671
##                     violent_crime_rate property_crime_rate pct_less_hs
## mean_pm                     0.05873094         0.088879773  0.14204622
## mean_o3                     0.02977242        -0.025156291  0.01633882
## pct_tree_cover             -0.20552631        -0.201827442 -0.19081045
## pct_impervious              0.31693831         0.246739067  0.33564418
## mean_aadt_intensity         0.11041575         0.074792588 -0.03883608
## dist_m_tri                 -0.06251962        -0.058223492 -0.37937630
## dist_m_npl                 -0.03185242        -0.152322474 -0.15916230
## dist_m_waste_site          -0.25287368        -0.268664603 -0.38800832
## dist_m_major_emit          -0.01789622        -0.209766780  0.21893159
## dist_m_cafo                 0.01675556        -0.064647236 -0.30067863
## dist_m_mine_well           -0.15245003        -0.056406808 -0.37449548
## cvd_rate_adj                0.47523468         0.211613232  0.57081344
## res_rate_adj                0.49944925         0.280786581  0.47040930
## violent_crime_rate          1.00000000         0.705151942  0.27967307
## property_crime_rate         0.70515194         1.000000000 -0.00684836
## pct_less_hs                 0.27967307        -0.006848360  1.00000000
## pct_unemp                   0.35971778         0.007623781  0.62343462
## pct_limited_eng             0.24385889        -0.050184228  0.80738433
## pct_hh_pov                  0.42127121         0.163143151  0.72420883
## pct_poc                     0.31980337        -0.053765481  0.81887450
##                        pct_unemp pct_limited_eng  pct_hh_pov     pct_poc
## mean_pm              0.032317153      0.08339659  0.10685820  0.11382369
## mean_o3              0.018969666      0.01164707 -0.01810003  0.01714269
## pct_tree_cover      -0.021515177     -0.10974662  0.01115617 -0.27177501
## pct_impervious       0.392914001      0.38111402  0.56509450  0.29005220
## mean_aadt_intensity  0.147397153      0.03855846  0.19888999  0.02408835
## dist_m_tri          -0.198747643     -0.25490796 -0.31558789 -0.30767438
## dist_m_npl           0.132536906      0.01801953 -0.03111065 -0.01906733
## dist_m_waste_site   -0.128623290     -0.22333346 -0.30045944 -0.16245202
## dist_m_major_emit    0.330098571      0.35547555  0.24950766  0.31155805
## dist_m_cafo         -0.030506530     -0.12570743 -0.01148631 -0.28558427
## dist_m_mine_well    -0.270526163     -0.27607853 -0.21843600 -0.51797735
## cvd_rate_adj         0.468277441      0.49057745  0.53848063  0.59759446
## res_rate_adj         0.441149256      0.38016497  0.55794450  0.39359867
## violent_crime_rate   0.359717785      0.24385889  0.42127121  0.31980337
## property_crime_rate  0.007623781     -0.05018423  0.16314315 -0.05376548
## pct_less_hs          0.623434625      0.80738433  0.72420883  0.81887450
## pct_unemp            1.000000000      0.61293958  0.68048090  0.64003145
## pct_limited_eng      0.612939575      1.00000000  0.74208323  0.74916462
## pct_hh_pov           0.680480902      0.74208323  1.00000000  0.62040136
## pct_poc              0.640031449      0.74916462  0.62040136  1.00000000
ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.3 Covariate data

Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.

NOTE: It’ll be interesting to see what comes out of our BEAMERS discussion re: adjusting for gestational age. It’s currently in the analysis

There are four continuous covariates; all of the others have been coded as dummy variables. For the dummy variables, the reference groups are: white_re, ed_grad, norm_bmi

W <- select(hs_data2, 
            lat, lon, lat_lon_int,
            latina_re, black_re, other_re,
            ed_no_hs, ed_hs, ed_aa, ed_4yr,
            low_bmi, ovwt_bmi, obese_bmi,
            concep_spring, concep_summer, concep_fall,
            concep_2010, concep_2011, concep_2012, concep_2013,
            maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
            male, gest_age_w) %>%
  as.matrix()
head(W)
##           lat       lon lat_lon_int latina_re black_re other_re ed_no_hs ed_hs
## [1,] 39.79402 -104.8133   -4170.944         1        0        0        0     0
## [2,] 39.62671 -104.9927   -4160.517         0        0        1        0     0
## [3,] 39.74934 -104.9129   -4170.219         0        0        0        0     0
## [4,] 39.68397 -104.8933   -4162.583         0        0        0        0     0
## [5,] 39.79134 -104.7669   -4168.814         0        1        0        0     0
## [6,] 39.68050 -104.9451   -4164.274         1        0        0        0     0
##      ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,]     1      0       0        0         0             0             0
## [2,]     1      0       0        0         0             0             0
## [3,]     0      0       0        0         0             0             0
## [4,]     1      0       0        0         0             1             0
## [5,]     0      1       0        0         0             1             0
## [6,]     1      0       0        0         0             0             0
##      concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,]           0           0           0           0           0           19
## [2,]           0           1           0           0           0           36
## [3,]           0           1           0           0           0           34
## [4,]           0           1           0           0           0           28
## [5,]           0           1           0           0           0           30
## [6,]           0           1           0           0           0           22
##      any_smoker smokeSH mean_cpss mean_epsd male gest_age_w
## [1,]          0       1        29         0    0   40.57143
## [2,]          0       0        19         2    1   35.85714
## [3,]          0       0        19         1    0   40.42857
## [4,]          0       0        20         0    0   36.28571
## [5,]          0       0        15         0    1   38.42857
## [6,]          0       0        17         1    0   40.71429

Scaled the non-binary (continuous) covariates

colnames(W)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"          "gest_age_w"
W.s <- apply(W[,c(1, 2, 3, 21, 24, 25, 27)], 2, scale) #' just the continuous ones

W.scaled <- cbind(W.s[,1:3],
                  W[,4:20], W.s[,4],
                  W[,22:23], W.s[,5:6],
                  W[,26], W.s[,7])
colnames(W.scaled)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] ""              "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     ""              ""
colnames(W.scaled) <- colnames(W)
head(W.scaled)
##             lat        lon lat_lon_int latina_re black_re other_re ed_no_hs
## [1,]  0.9587536  0.5410850  -0.5821980         1        0        0        0
## [2,] -1.5498523 -1.6236392   0.6519093         0        0        1        0
## [3,]  0.2887793 -0.6606299  -0.4964164         0        0        0        0
## [4,] -0.6913627 -0.4239607   0.4073829         0        0        0        0
## [5,]  0.9185421  1.1019032  -0.3300513         0        1        0        0
## [6,] -0.7433125 -1.0489343   0.2071583         1        0        0        0
##      ed_hs ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,]     0     1      0       0        0         0             0             0
## [2,]     0     1      0       0        0         0             0             0
## [3,]     0     0      0       0        0         0             0             0
## [4,]     0     1      0       0        0         0             1             0
## [5,]     0     0      1       0        0         0             1             0
## [6,]     0     1      0       0        0         0             0             0
##      concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,]           0           0           0           0           0  -1.39815187
## [2,]           0           1           0           0           0   1.35109608
## [3,]           0           1           0           0           0   1.02765515
## [4,]           0           1           0           0           0   0.05733234
## [5,]           0           1           0           0           0   0.38077328
## [6,]           0           1           0           0           0  -0.91299047
##      any_smoker smokeSH  mean_cpss  mean_epsd male gest_age_w
## [1,]          0       1  3.3147856 -1.2832098    0  0.7037686
## [2,]          0       0  0.1179652 -0.6860171    1 -1.9146645
## [3,]          0       0  0.1179652 -0.9846134    0  0.6244221
## [4,]          0       0  0.4376472 -1.2832098    0 -1.6766251
## [5,]          0       0 -1.1607630 -1.2832098    1 -0.4864283
## [6,]          0       0 -0.5213989 -0.9846134    0  0.7831150
summary(W.scaled)
##       lat                lon           lat_lon_int         latina_re     
##  Min.   :-2.45418   Min.   :-2.5043   Min.   :-3.48430   Min.   :0.0000  
##  1st Qu.:-0.62577   1st Qu.:-0.5848   1st Qu.:-0.48738   1st Qu.:0.0000  
##  Median : 0.03151   Median : 0.1214   Median : 0.02121   Median :0.0000  
##  Mean   : 0.00000   Mean   : 0.0000   Mean   : 0.00000   Mean   :0.2653  
##  3rd Qu.: 0.42402   3rd Qu.: 0.6654   3rd Qu.: 0.60627   3rd Qu.:1.0000  
##  Max.   : 4.00304   Max.   : 4.5531   Max.   : 2.60273   Max.   :1.0000  
##     black_re         other_re          ed_no_hs          ed_hs       
##  Min.   :0.0000   Min.   :0.00000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.00000   Median :0.0000   Median :0.0000  
##  Mean   :0.1717   Mean   :0.06689   Mean   :0.1527   Mean   :0.1851  
##  3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.00000   Max.   :1.0000   Max.   :1.0000  
##      ed_aa            ed_4yr          low_bmi           ovwt_bmi    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.000  
##  Median :0.0000   Median :0.0000   Median :0.00000   Median :0.000  
##  Mean   :0.2319   Mean   :0.2185   Mean   :0.03344   Mean   :0.262  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:1.000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.00000   Max.   :1.000  
##    obese_bmi      concep_spring    concep_summer     concep_fall    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.1996   Mean   :0.2497   Mean   :0.2408   Mean   :0.2709  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##   concep_2010      concep_2011      concep_2012      concep_2013    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.1616   Mean   :0.3021   Mean   :0.2932   Mean   :0.2419  
##  3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##   maternal_age        any_smoker         smokeSH         mean_cpss      
##  Min.   :-1.88331   Min.   :0.00000   Min.   :0.0000   Min.   :-5.9560  
##  1st Qu.:-0.91299   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:-0.5214  
##  Median : 0.05733   Median :0.00000   Median :0.0000   Median : 0.0114  
##  Mean   : 0.00000   Mean   :0.08696   Mean   :0.2575   Mean   : 0.0000  
##  3rd Qu.: 0.70421   3rd Qu.:0.00000   3rd Qu.:1.0000   3rd Qu.: 0.5442  
##  Max.   : 2.64486   Max.   :1.00000   Max.   :1.0000   Max.   : 4.5935  
##    mean_epsd            male          gest_age_w     
##  Min.   :-1.2832   Min.   :0.0000   Min.   :-7.7070  
##  1st Qu.:-0.7855   1st Qu.:0.0000   1st Qu.:-0.3277  
##  Median :-0.1884   Median :1.0000   Median : 0.1483  
##  Mean   : 0.0000   Mean   :0.5117   Mean   : 0.0000  
##  3rd Qu.: 0.6079   3rd Qu.:1.0000   3rd Qu.: 0.6244  
##  Max.   : 6.0324   Max.   :1.0000   Max.   : 2.9255

Variance and histograms for the scaled covariates

var(W.scaled)
##                         lat            lon   lat_lon_int      latina_re
## lat            1.0000000000 -0.25261855699 -0.9261702843  0.02075377736
## lon           -0.2526185570  1.00000000000  0.5988415501  0.01061991294
## lat_lon_int   -0.9261702843  0.59884155012  1.0000000000 -0.01302007756
## latina_re      0.0207537774  0.01061991294 -0.0130200776  0.19514701784
## black_re      -0.0122649034  0.04784916212  0.0288174353 -0.04560340022
## other_re      -0.0009403195 -0.00123694771  0.0002902002 -0.01776755853
## ed_no_hs       0.0058668471  0.01732912905  0.0019047436  0.03978788422
## ed_hs         -0.0130652792  0.04117136599  0.0268694085  0.02896808807
## ed_aa         -0.0071789427  0.04676104709  0.0241824221  0.01318258282
## ed_4yr         0.0022352364 -0.00766878563 -0.0048607788 -0.03571926262
## low_bmi       -0.0029774584 -0.00003551643  0.0024531145  0.00004479216
## ovwt_bmi       0.0205880066  0.00512460048 -0.0150602639  0.02081218148
## obese_bmi      0.0165669344  0.00976713009 -0.0098964732  0.02065416468
## concep_spring  0.0143292896 -0.00046075172 -0.0120393632 -0.00606436136
## concep_summer -0.0140319053 -0.00711327850  0.0088444045 -0.00481142499
## concep_fall    0.0054905592  0.01642183233  0.0018457750  0.01732710225
## concep_2010    0.0110681241  0.00844610317 -0.0058861055 -0.00610790930
## concep_2011   -0.0220635440  0.01869831001  0.0255410960 -0.00882156792
## concep_2012    0.0024435961 -0.00706763788 -0.0047707939  0.01252065416
## concep_2013    0.0074817863 -0.02068066481 -0.0142344221  0.00158887761
## maternal_age   0.0307789398 -0.17980907079 -0.0955945618 -0.10858833047
## any_smoker    -0.0082274331  0.02279799333  0.0156963705 -0.00858889752
## smokeSH       -0.0111042258  0.04668855425  0.0273846128 -0.00590510033
## mean_cpss     -0.0258360855 -0.01114736129  0.0170462313 -0.04668314421
## mean_epsd     -0.0347375477  0.05084465609  0.0485855489  0.04322362524
## male           0.0290047629 -0.02552947737 -0.0339519192 -0.00087717989
## gest_age_w     0.0111191604 -0.03926647196 -0.0245324539 -0.02639363168
##                    black_re      other_re      ed_no_hs          ed_hs
## lat           -0.0122649034 -0.0009403195  0.0058668471 -0.01306527915
## lon            0.0478491621 -0.0012369477  0.0173291290  0.04117136599
## lat_lon_int    0.0288174353  0.0002902002  0.0019047436  0.02686940852
## latina_re     -0.0456034002 -0.0177675585  0.0397878842  0.02896808807
## black_re       0.1423669175 -0.0114966555  0.0128118032  0.01506758640
## other_re      -0.0114966555  0.0624850693 -0.0035311156  0.00658071548
## ed_no_hs       0.0128118032 -0.0035311156  0.1295488931 -0.02829620561
## ed_hs          0.0150675864  0.0065807155 -0.0282962056  0.15098194378
## ed_aa          0.0192967133  0.0023291925 -0.0354554865 -0.04296066253
## ed_4yr        -0.0163503842 -0.0034713927 -0.0334099777 -0.04048216276
## low_bmi        0.0020641722 -0.0011235368 -0.0039977007 -0.00173196369
## ovwt_bmi      -0.0003857103 -0.0052668120  0.0045849757 -0.00612657270
## obese_bmi      0.0069962872  0.0022620043  0.0063181836  0.02441297380
## concep_spring  0.0017220099  0.0044829491 -0.0002364031  0.00395788541
## concep_summer -0.0079058170  0.0017319637 -0.0044530877 -0.00331835284
## concep_fall   -0.0063828834 -0.0047479694  0.0110338032  0.00226573698
## concep_2010    0.0090467730 -0.0007801302 -0.0001629937  0.00576574693
## concep_2011    0.0183859392 -0.0023739847  0.0096091635 -0.00463350056
## concep_2012   -0.0146793876  0.0004553870 -0.0035360925  0.00371526119
## concep_2013   -0.0125617136  0.0027733815 -0.0057396182 -0.00464096592
## maternal_age  -0.0895968722 -0.0133074822 -0.1376124653 -0.10868310364
## any_smoker     0.0185364907 -0.0013586957  0.0179541925  0.00174689441
## smokeSH        0.0349789477  0.0084246596  0.0309364548  0.02483352246
## mean_cpss     -0.0233123370  0.0255604593 -0.0561153540 -0.03433895561
## mean_epsd      0.0220578552  0.0202679881  0.0670107276  0.02014619096
## male           0.0002202281  0.0003322086 -0.0135085702  0.00006345557
## gest_age_w    -0.0368471269 -0.0054750903 -0.0076928484 -0.01723767893
##                      ed_aa        ed_4yr        low_bmi      ovwt_bmi
## lat           -0.007178943  0.0022352364 -0.00297745845  0.0205880066
## lon            0.046761047 -0.0076687856 -0.00003551643  0.0051246005
## lat_lon_int    0.024182422 -0.0048607788  0.00245311454 -0.0150602639
## latina_re      0.013182583 -0.0357192626  0.00004479216  0.0208121815
## black_re       0.019296713 -0.0163503842  0.00206417224 -0.0003857103
## other_re       0.002329193 -0.0034713927 -0.00112353679 -0.0052668120
## ed_no_hs      -0.035455487 -0.0334099777 -0.00399770067  0.0045849757
## ed_hs         -0.042960663 -0.0404821628 -0.00173196369 -0.0061265727
## ed_aa          0.178312629 -0.0507246377  0.00786102484  0.0150750518
## ed_4yr        -0.050724638  0.1709517837 -0.00173569637  0.0040748427
## low_bmi        0.007861025 -0.0017356964  0.03236233875 -0.0087717989
## ovwt_bmi       0.015075052  0.0040748427 -0.00877179885  0.1935643614
## obese_bmi      0.009478520 -0.0124024526 -0.00668149785 -0.0523383998
## concep_spring  0.006761128 -0.0066354615 -0.00501298973  0.0092806876
## concep_summer -0.011257764  0.0064762004  0.00309812470 -0.0051212375
## concep_fall   -0.007084627  0.0010078237  0.00320637243  0.0026091436
## concep_2010    0.004884834  0.0003533604  0.00128404204 -0.0033345278
## concep_2011    0.002410067  0.0053402214  0.00439336479  0.0055828456
## concep_2012   -0.005564182 -0.0061016882 -0.00535266364 -0.0043547938
## concep_2013   -0.002587992  0.0006519748 -0.00028741639  0.0023988692
## maternal_age  -0.040296710  0.1091044519 -0.01089529356  0.0089002276
## any_smoker     0.011063665 -0.0156735248  0.00155279503 -0.0060656056
## smokeSH        0.022806677 -0.0362443263  0.00142215122 -0.0106232083
## mean_cpss      0.030714793  0.0282429323  0.00484169668 -0.0082476896
## mean_epsd      0.025424770 -0.0463684315  0.00946748435 -0.0019127169
## male           0.000630823  0.0063679527 -0.00262407430  0.0008361204
## gest_age_w    -0.035168407  0.0301476493 -0.00601412877 -0.0148466585
##                   obese_bmi concep_spring  concep_summer   concep_fall
## lat            0.0165669344  0.0143292896 -0.01403190526  0.0054905592
## lon            0.0097671301 -0.0004607517 -0.00711327850  0.0164218323
## lat_lon_int   -0.0098964732 -0.0120393632  0.00884440451  0.0018457750
## latina_re      0.0206541647 -0.0060643614 -0.00481142499  0.0173271022
## black_re       0.0069962872  0.0017220099 -0.00790581701 -0.0063828834
## other_re       0.0022620043  0.0044829491  0.00173196369 -0.0047479694
## ed_no_hs       0.0063181836 -0.0002364031 -0.00445308767  0.0110338032
## ed_hs          0.0244129738  0.0039578854 -0.00331835284  0.0022657370
## ed_aa          0.0094785197  0.0067611284 -0.01125776398 -0.0070846273
## ed_4yr        -0.0124024526 -0.0066354615  0.00647620043  0.0010078237
## low_bmi       -0.0066814978 -0.0050129897  0.00309812470  0.0032063724
## ovwt_bmi      -0.0523383998  0.0092806876 -0.00512123746  0.0026091436
## obese_bmi      0.1599105152 -0.0085938744 -0.00346392738  0.0005673674
## concep_spring -0.0085938744  0.1875696767 -0.06020066890 -0.0677257525
## concep_summer -0.0034639274 -0.0602006689  0.18302078356 -0.0653069756
## concep_fall    0.0005673674 -0.0677257525 -0.06530697563  0.1977350096
## concep_2010   -0.0043921206 -0.0236714146  0.00009331701  0.0287043120
## concep_2011    0.0032598742  0.0003633142 -0.00140348782 -0.0127396381
## concep_2012    0.0072737498 -0.0085677457  0.00186260750  0.0019559245
## concep_2013   -0.0059187868  0.0321545529 -0.00028368371 -0.0176182513
## maternal_age   0.0027900741 -0.0149065532  0.01490413862 -0.0196470231
## any_smoker     0.0027173913  0.0016983696  0.00024262422 -0.0023777174
## smokeSH        0.0110524666 -0.0041134138 -0.00627836837 -0.0028778966
## mean_cpss     -0.0087226114  0.0079650833  0.01166899615 -0.0055888831
## mean_epsd      0.0281330380 -0.0063209443 -0.01563660013  0.0265650931
## male          -0.0017804885 -0.0062746357 -0.00393797778  0.0018476768
## gest_age_w    -0.0214614301 -0.0179961830  0.01920131892  0.0141959621
##                  concep_2010   concep_2011  concep_2012   concep_2013
## lat            0.01106812411 -0.0220635440  0.002443596  0.0074817863
## lon            0.00844610317  0.0186983100 -0.007067638 -0.0206806648
## lat_lon_int   -0.00588610547  0.0255410960 -0.004770794 -0.0142344221
## latina_re     -0.00610790930 -0.0088215679  0.012520654  0.0015888776
## black_re       0.00904677297  0.0183859392 -0.014679388 -0.0125617136
## other_re      -0.00078013020 -0.0023739847  0.000455387  0.0027733815
## ed_no_hs      -0.00016299371  0.0096091635 -0.003536093 -0.0057396182
## ed_hs          0.00576574693 -0.0046335006  0.003715261 -0.0046409659
## ed_aa          0.00488483437  0.0024100673 -0.005564182 -0.0025879917
## ed_4yr         0.00035336041  0.0053402214 -0.006101688  0.0006519748
## low_bmi        0.00128404204  0.0043933648 -0.005352664 -0.0002874164
## ovwt_bmi      -0.00333452779  0.0055828456 -0.004354794  0.0023988692
## obese_bmi     -0.00439212056  0.0032598742  0.007273750 -0.0059187868
## concep_spring -0.02367141464  0.0003633142 -0.008567746  0.0321545529
## concep_summer  0.00009331701 -0.0014034878  0.001862608 -0.0002836837
## concep_fall    0.02870431199 -0.0127396381  0.001955925 -0.0176182513
## concep_2010    0.13567048893 -0.0488918916 -0.047448589 -0.0391495959
## concep_2011   -0.04889189162  0.2110780976 -0.088679776 -0.0731692447
## concep_2012   -0.04744858855 -0.0886797758  0.207464863 -0.0710092670
## concep_2013   -0.03914959588 -0.0731692447 -0.071009267  0.1835981048
## maternal_age  -0.02663971411 -0.0380704459  0.031448396  0.0348222009
## any_smoker     0.00266886646  0.0105298913 -0.011015140 -0.0020865683
## smokeSH        0.00631569517  0.0136280160 -0.018670867 -0.0021014990
## mean_cpss      0.00832724099 -0.0113573536 -0.011161856  0.0104924310
## mean_epsd     -0.01748485806  0.0347867417 -0.022850868  0.0069811381
## male           0.00089584329 -0.0029824116 -0.001761825  0.0044194935
## gest_age_w     0.01072301448 -0.0118973482 -0.026416733  0.0268056111
##               maternal_age    any_smoker      smokeSH    mean_cpss    mean_epsd
## lat            0.030778940 -0.0082274331 -0.011104226 -0.025836085 -0.034737548
## lon           -0.179809071  0.0227979933  0.046688554 -0.011147361  0.050844656
## lat_lon_int   -0.095594562  0.0156963705  0.027384613  0.017046231  0.048585549
## latina_re     -0.108588330 -0.0085888975 -0.005905100 -0.046683144  0.043223625
## black_re      -0.089596872  0.0185364907  0.034978948 -0.023312337  0.022057855
## other_re      -0.013307482 -0.0013586957  0.008424660  0.025560459  0.020267988
## ed_no_hs      -0.137612465  0.0179541925  0.030936455 -0.056115354  0.067010728
## ed_hs         -0.108683104  0.0017468944  0.024833522 -0.034338956  0.020146191
## ed_aa         -0.040296710  0.0110636646  0.022806677  0.030714793  0.025424770
## ed_4yr         0.109104452 -0.0156735248 -0.036244326  0.028242932 -0.046368432
## low_bmi       -0.010895294  0.0015527950  0.001422151  0.004841697  0.009467484
## ovwt_bmi       0.008900228 -0.0060656056 -0.010623208 -0.008247690 -0.001912717
## obese_bmi      0.002790074  0.0027173913  0.011052467 -0.008722611  0.028133038
## concep_spring -0.014906553  0.0016983696 -0.004113414  0.007965083 -0.006320944
## concep_summer  0.014904139  0.0002426242 -0.006278368  0.011668996 -0.015636600
## concep_fall   -0.019647023 -0.0023777174 -0.002877897 -0.005588883  0.026565093
## concep_2010   -0.026639714  0.0026688665  0.006315695  0.008327241 -0.017484858
## concep_2011   -0.038070446  0.0105298913  0.013628016 -0.011357354  0.034786742
## concep_2012    0.031448396 -0.0110151398 -0.018670867 -0.011161856 -0.022850868
## concep_2013    0.034822201 -0.0020865683 -0.002101499  0.010492431  0.006981138
## maternal_age   1.000000000 -0.0466296108 -0.155964054  0.100637638 -0.160410684
## any_smoker    -0.046629611  0.0794836957  0.049010093  0.017642908  0.042144665
## smokeSH       -0.155964054  0.0490100932  0.191419314  0.031721118  0.108180210
## mean_cpss      0.100637638  0.0176429080  0.031721118  1.000000000  0.455187203
## mean_epsd     -0.160410684  0.0421446647  0.108180210  0.455187203  1.000000000
## male           0.023413804  0.0023291925  0.002004449 -0.003315304  0.001541815
## gest_age_w     0.091663607 -0.0149814181 -0.050311537 -0.037142336 -0.137187808
##                         male   gest_age_w
## lat            0.02900476291  0.011119160
## lon           -0.02552947737 -0.039266472
## lat_lon_int   -0.03395191918 -0.024532454
## latina_re     -0.00087717989 -0.026393632
## black_re       0.00022022814 -0.036847127
## other_re       0.00033220855 -0.005475090
## ed_no_hs      -0.01350857023 -0.007692848
## ed_hs          0.00006345557 -0.017237679
## ed_aa          0.00063082298 -0.035168407
## ed_4yr         0.00636795270  0.030147649
## low_bmi       -0.00262407430 -0.006014129
## ovwt_bmi       0.00083612040 -0.014846658
## obese_bmi     -0.00178048853 -0.021461430
## concep_spring -0.00627463569 -0.017996183
## concep_summer -0.00393797778  0.019201319
## concep_fall    0.00184767678  0.014195962
## concep_2010    0.00089584329  0.010723014
## concep_2011   -0.00298241161 -0.011897348
## concep_2012   -0.00176182513 -0.026416733
## concep_2013    0.00441949355  0.026805611
## maternal_age   0.02341380415  0.091663607
## any_smoker     0.00232919255 -0.014981418
## smokeSH        0.00200444935 -0.050311537
## mean_cpss     -0.00331530432 -0.037142336
## mean_epsd      0.00154181454 -0.137187808
## male           0.25014184185 -0.007427180
## gest_age_w    -0.00742717951  1.000000000
ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.4 Response data: birth weight (in grams)

Y <- select(hs_data2, birth_weight) %>%
  as.matrix()
head(Y)
##      birth_weight
## [1,]         2860
## [2,]         2755
## [3,]         3505
## [4,]         2695
## [5,]         3355
## [6,]         3810

Distribution of birth weight and scaled birth weight

hist(Y, breaks = 20)

hist(scale(Y), breaks = 20)

1.5 Scatterplots of exposures and outcome (birth weight)

Both birth weight (Y) and the exposures are scaled here

NOTE: Don’t use these plots as a way to estimate how many predictors might make the cut. This should be done a priori

df <- as.data.frame(cbind(scale(Y), X.scaled))
# par(mfrow=c(5,4))
sapply(2:length(df), function(x){
  lm.x <- lm(birth_weight ~ df[,x], data = df)
  plot(df[,c(x, 1)],
       xlab = paste0(colnames(df)[x], " beta: ",
                     round(summary(lm.x)$coef[2,1],4),
                     "; p = ",
                     round(summary(lm.x)$coef[2,4],4)))
  abline(lm.x)
})

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2 Is gestational age a potenital mediator?

I.e., is there a relationship between our exposures and gestational age?

The DAG might look something like this:

exposures —> gestational age —> birth weight _________________________________^

2.1 Scatter plots for exposures and gestational age

Both gestational age and the exposures are scaled here. Gestational age measured in weeks from estimated date of conception to delivery

Since there were some (small) relationships between exposures and gestational age (based on simple linear regression models– namely the ozone and SES indicators), I’m going to omit this covariate for now.

df2 <- as.data.frame(cbind(W.scaled[,"gest_age_w"], X.scaled))
colnames(df2)[1] <- "gest_age_w"
# par(mfrow=c(5,4))
sapply(2:length(df2), function(x){
  lm.x <- lm(gest_age_w ~ df2[,x], data = df2)
  plot(df2[,c(x, 1)],
       xlab = paste0(colnames(df2)[x], " beta: ",
                     round(summary(lm.x)$coef[2,1],4),
                     "; p = ",
                     round(summary(lm.x)$coef[2,4],4)))
  abline(lm.x)
})

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Dropping gest_age_w from the covariates

W.scaled2 <- W.scaled[,-c(ncol(W.scaled))]
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"

3 RIDGE regression

To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.

set.seed(123)

library(glmnet)
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack
## Loaded glmnet 4.0-2
lambda_seq <- 10^seq(4, -4, by = -.05)

#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
                      standardize = T, standardize.response = T)
plot(ridge_cv)

best_lambda <- ridge_cv$lambda.min
best_lambda
## [1] 630.9573
#' Fit the model using the best_lambda
bw_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
                   standardize = T, standardize.response = T)
summary(bw_ridge)
##           Length Class     Mode   
## a0         1     -none-    numeric
## beta      20     dgCMatrix S4     
## df         1     -none-    numeric
## dim        2     -none-    numeric
## lambda     1     -none-    numeric
## dev.ratio  1     -none-    numeric
## nulldev    1     -none-    numeric
## npasses    1     -none-    numeric
## jerr       1     -none-    numeric
## offset     1     -none-    logical
## call       7     -none-    call   
## nobs       1     -none-    numeric

Ridge regression coefficients

coef(bw_ridge)
## 21 x 1 sparse Matrix of class "dgCMatrix"
##                                  s0
## (Intercept)         3764.2974431484
## mean_pm                7.7753350262
## mean_o3               -8.5947719688
## pct_tree_cover        -0.0074346757
## pct_impervious        -0.4874093432
## mean_aadt_intensity   -0.0003363759
## dist_m_tri            -0.0005811201
## dist_m_npl             0.0002060546
## dist_m_waste_site      0.0021158752
## dist_m_major_emit     -0.0002875616
## dist_m_cafo           -0.0003386587
## dist_m_mine_well      -0.0032347267
## cvd_rate_adj          -0.1632413722
## res_rate_adj          -0.1502653198
## violent_crime_rate    -0.3428576912
## property_crime_rate   -0.0247667418
## pct_less_hs           -0.7383109357
## pct_unemp             -4.4184536971
## pct_limited_eng       -0.4337403128
## pct_hh_pov            -0.4325335405
## pct_poc               -0.5119074150

Ridge regression predictions

ridge_pred <- predict(bw_ridge, newx = X)
plot(Y, ridge_pred)

actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))

The R2 value for this model is 0.03. Based on these results, it doesn’t look like there’s much here.

4 Nonparametric Bayesian Shrinkage (NPB): Birth weight

Still, we wanted to try to fit the NPB model with these data.

4.1 Finding the NPB priors

Start with Lauren’s from the example in the vignette

In an email from April 29, Lauren provided me with some additional guidance on finding the NPB priors:

  • Keep alpha.pi and beta.pi set to 1, and then let a.phi1 take values 1, 10, and 100 and see how the results change.
  • Keep a.phi1 set to 1 (or 10 or 100), and mess with alpha.pi and beta.pi.
    • Run the following code: alpha.pi=1 beta.pi=1 plot(density(rbeta(10000, alpha.pi, beta.pi))) and then change alpha.pi and beta.pi and see how it changes the prior distribution.
    • This is the distribution of the probability of a main effect regression coefficient being 0 (aka exclusion probability). We don’t want this to be too informative (you don’t want high mass around just a few values). Also alpha.pi and beta.pi don’t have to be the same value. You might try alpha.pi = 1 and beta.pi = 2 to get a slightly lower prior probability of exclusion. Try not to change all three (alpha.pi, beta.pi, and a.phi1) at once.
  • When playing with the priors, set “interact=FALSE” and just fit the modelwith the main effects. Most of the interactions were null anyway so it shouldn’t change the results too much and it will make the code run a lot faster. Then when you find a set of priors you like, you can add in “interact=TRUE” and “XWinteract=TRUE.”

Some additional feedback from Lauren during our 6/10 meeting:

  • The confidence intervals were really wide and heavily skewed. I’m going to try adjusting the sig2inv.mu1 parameter after the a.phi1 parameter to see if this helps
  • the rbeta distributions is interpreted as the exclusion probability, so I should try to aim to have most of the mass of that distribution in the middle, since we hypothesize that maybe 40-60% of the predictors will be important. The way to do this is to set alpha.pi and beta.pi to the same value
  • I should set the burn in number to be about half the iterations

Note: I’m including far fewer iterations of the priors than in the previous version of the document.

4.1.1 Vignette Priors

set.seed(123)

priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1)

fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]    0.127441460 2.6609141     0.000000            0 0.026
##  [2,]   -0.963719549 8.8753281    -1.526898            0 0.034
##  [3,]    0.029752904 1.6712101     0.000000            0 0.016
##  [4,]   -0.055071939 0.6099851     0.000000            0 0.012
##  [5,]    0.169061015 2.5847844     0.000000            0 0.008
##  [6,]    0.053765120 2.4427873     0.000000            0 0.010
##  [7,]    0.141469800 2.3645803     0.000000            0 0.024
##  [8,]    0.462321176 4.3762285     0.000000            0 0.034
##  [9,]   -0.001465069 1.4819965     0.000000            0 0.016
## [10,]   -0.118832429 3.3222775     0.000000            0 0.020
## [11,]   -0.160301912 2.5767658     0.000000            0 0.024
## [12,]   -0.072292473 1.7048618     0.000000            0 0.018
## [13,]   -0.105399537 2.0370932     0.000000            0 0.018
## [14,]   -0.073266119 2.0667136     0.000000            0 0.018
## [15,]   -0.027547929 0.8532218     0.000000            0 0.020
## [16,]    0.008342958 1.8775514     0.000000            0 0.018
## [17,]   -0.606745402 4.5618241    -3.743610            0 0.032
## [18,]   -0.009390117 1.4188808     0.000000            0 0.014
## [19,]   -0.028581985 0.8229871     0.000000            0 0.014
## [20,]   -0.120797095 1.2799276     0.000000            0 0.026
plot(fit.npb.1$beta[,1], type = "l")

plot(fit.npb.1$beta[,2], type = "l")

plot(fit.npb.1$beta[,13], type = "l")

4.1.2 Adjust alpha.pi and beta.pi

For now, leave a.phi1 and sig2inv.mu1 alone for now.

alpha.pi and beta.pi are responisble for the exclusion probability distribution. If we thing we want ~50% of our covariates, we need the mass of this distribution to be somewhere between 0.4 and 0.6. To do this, we set alpha.pi and beta.pi to the same value

4.1.2.1 Try making alpha.pi and beta.pi 2

plot(density(rbeta(10000, 2, 2)))

priors.npb.12 <- list(alpha.pi = 2, beta.pi = 2, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1, sig2inv.mu1 = 1)

fit.npb.12 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.12, interact = F)
npb.sum.12 <- summary(fit.npb.12)
npb.sum.12$main.effects
##       Posterior Mean       SD 95% CI Lower 95% CI Upper   PIP
##  [1,]    0.031460972 2.759754    0.0000000      0.00000 0.036
##  [2,]   -1.106775179 8.286496   -9.3607570      0.00000 0.048
##  [3,]   -0.071148608 1.803463    0.0000000      0.00000 0.030
##  [4,]   -0.212002282 1.877947    0.0000000      0.00000 0.032
##  [5,]    0.103107143 2.919152    0.0000000      0.00000 0.024
##  [6,]   -0.017910531 2.646031   -1.6968561      0.00000 0.040
##  [7,]   -0.023801697 1.266272    0.0000000      0.00000 0.030
##  [8,]    1.038432554 6.790843    0.0000000     19.33131 0.056
##  [9,]    0.047453723 1.878220    0.0000000      0.00000 0.028
## [10,]   -0.479271478 7.450079   -5.9197197      0.00000 0.046
## [11,]   -0.436139635 3.614531   -5.5220092      0.00000 0.058
## [12,]   -0.222781424 2.613901   -4.1434755      0.00000 0.040
## [13,]   -0.423866505 3.383142   -4.6391150      0.00000 0.052
## [14,]   -0.028696447 1.399109    0.0000000      0.00000 0.028
## [15,]   -0.385945760 2.788175   -4.6318980      0.00000 0.046
## [16,]   -0.328050395 2.710702   -4.3542325      0.00000 0.050
## [17,]   -1.713017799 7.939331  -28.1312295      0.00000 0.092
## [18,]   -0.190778711 1.671843   -0.7519376      0.00000 0.038
## [19,]   -0.333680654 2.854248   -4.4999921      0.00000 0.058
## [20,]    0.004390389 4.393540    0.0000000      0.00000 0.030
plot(fit.npb.12$beta[,1], type = "l")

plot(fit.npb.12$beta[,2], type = "l")

plot(fit.npb.12$beta[,13], type = "l")

4.1.2.2 Try making alpha.pi and beta.pi 5

plot(density(rbeta(10000, 5, 5)))

priors.npb.13 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1, sig2inv.mu1 = 1)

fit.npb.13 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.13, interact = F)
npb.sum.13 <- summary(fit.npb.13)
npb.sum.13$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]    -0.42988258  5.099271   -12.173939    7.3648286 0.218
##  [2,]    -2.15655907  8.493732   -29.545431    5.5182644 0.252
##  [3,]    -0.37768748  4.028902    -9.478056    6.3596266 0.182
##  [4,]    -1.06819301  4.527702   -14.067572    3.9656823 0.208
##  [5,]    -0.05635313  4.033547    -7.708414    7.8425320 0.198
##  [6,]    -0.35015332  4.694971   -10.378587    7.3842082 0.240
##  [7,]     0.01706464  3.583146    -7.870653    7.9917422 0.188
##  [8,]     1.89609039 10.160326    -7.972503   27.9486549 0.258
##  [9,]    -0.09853021  4.475731    -8.469732    7.2192917 0.198
## [10,]    -0.75705052  8.136366   -17.109856   18.2214526 0.300
## [11,]    -1.95553682  7.597143   -18.455183    5.7648459 0.274
## [12,]    -1.00933065  5.070416   -15.617421    5.7672188 0.234
## [13,]    -2.07989371  7.125055   -22.524249    2.5222388 0.228
## [14,]    -0.57502090  3.454515    -9.412140    5.2100416 0.202
## [15,]    -1.55139794  5.453769   -15.555001    3.9013770 0.238
## [16,]    -1.24221196  5.027768   -16.604305    0.2111787 0.208
## [17,]    -3.69262176  9.960522   -37.080086    0.2158329 0.306
## [18,]    -1.08529982  4.555619   -11.956445    2.3442693 0.214
## [19,]    -1.23624033  5.294009   -13.787500    4.2793005 0.222
## [20,]    -0.66889158  5.208466   -14.717921    6.8705824 0.202
plot(fit.npb.13$beta[,1], type = "l")

plot(fit.npb.13$beta[,2], type = "l")

plot(fit.npb.13$beta[,13], type = "l")

4.1.2.3 Try making alpha.pi and beta.pi 8

plot(density(rbeta(10000, 8, 8)))

priors.npb.14 <- list(alpha.pi = 8, beta.pi = 8, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1, sig2inv.mu1 = 1)

fit.npb.14 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.14, interact = F)
npb.sum.14 <- summary(fit.npb.14)
npb.sum.14$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]    -0.21728605  4.841955   -10.179889    12.293195 0.294
##  [2,]    -3.25577064 10.082421   -35.532776     6.413138 0.424
##  [3,]    -0.06555033  5.603873   -10.942005    14.865837 0.356
##  [4,]    -0.91170821  5.266306   -12.338381     5.540108 0.304
##  [5,]     0.01164678  4.372853    -8.999654    13.182631 0.316
##  [6,]     0.18146622  5.109335   -10.637517    12.154360 0.326
##  [7,]     0.37243590  5.087502    -9.224864    14.704406 0.328
##  [8,]     1.82211841  7.556446    -6.276737    23.661811 0.336
##  [9,]     0.10194613  4.777040    -9.447546    12.483608 0.334
## [10,]    -1.25182172  8.250094   -17.901721    11.479718 0.376
## [11,]    -1.82782653  6.595916   -18.275559     8.724371 0.376
## [12,]    -1.36762029  6.085761   -14.170951     5.396575 0.348
## [13,]    -2.13267396  6.748211   -20.167041     5.214743 0.344
## [14,]    -0.30514401  4.956926   -11.058168    11.052763 0.290
## [15,]    -1.30796494  5.087459   -14.437606     7.237096 0.344
## [16,]    -0.89661097  5.145199   -13.904670     9.377070 0.328
## [17,]    -5.04483807 13.520294   -53.648764     3.448858 0.398
## [18,]    -0.85045895  5.610258   -12.243419     9.569949 0.360
## [19,]    -0.98827795  5.354069   -15.747970    10.067388 0.324
## [20,]    -0.76106064  5.467010   -12.798167     8.479743 0.322
plot(fit.npb.14$beta[,1], type = "l")

plot(fit.npb.14$beta[,2], type = "l")

plot(fit.npb.14$beta[,13], type = "l")

4.1.3 Set alpha.pi and beta.pi to 5, readjust a.phi1 and sig2inv.mu1

Set alpha.pi and beta.pi to 5, rather than 8, and try adjusting a.phi1 and sig2inv.mu1

4.1.3.1 Try making a.phi1 = 10 and sig2inv.mu1 = 1

priors.npb.23 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 10, sig2inv.mu1 = 1)

fit.npb.23 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.23, interact = F)
npb.sum.23 <- summary(fit.npb.23)
npb.sum.23$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]      0.1069866  6.030672   -10.554858    13.131595 0.238
##  [2,]     -3.5388600 11.344879   -45.538900     4.235505 0.322
##  [3,]     -0.4768194  4.979254   -12.315786     9.407688 0.228
##  [4,]     -1.0777163  6.297829   -15.527336     7.048780 0.254
##  [5,]      0.3079882  4.895994    -9.898415    16.016525 0.232
##  [6,]     -0.1230844  3.855826    -9.979027     8.495729 0.230
##  [7,]      0.3294762  4.952409    -9.520599    12.258212 0.276
##  [8,]      2.5225039  9.778397    -7.572233    32.624945 0.288
##  [9,]      0.6895912  5.797225    -8.017044    18.542429 0.228
## [10,]     -1.6739128 14.608443   -31.912931    10.597203 0.256
## [11,]     -1.7041623  8.389439   -30.507136     7.118220 0.292
## [12,]     -1.0759523  5.811060   -14.993317     7.160186 0.258
## [13,]     -0.9631344  5.189698   -14.977589     7.118220 0.230
## [14,]      0.0395097  5.946596   -11.826354    16.200728 0.248
## [15,]     -1.1190244  5.436167   -19.009897     4.634652 0.260
## [16,]     -0.4465094  5.720176   -15.167128    10.170565 0.232
## [17,]     -8.0200614 17.258083   -60.986895     2.233433 0.396
## [18,]     -0.7233699  5.161727   -12.113457     6.502124 0.228
## [19,]     -0.4769079  4.910888   -12.700919     5.732387 0.220
## [20,]      0.3297563  5.004282    -8.627797    15.102298 0.218
plot(fit.npb.23$beta[,1], type = "l")

plot(fit.npb.23$beta[,2], type = "l")

plot(fit.npb.23$beta[,13], type = "l")

4.1.3.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10

priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 10, sig2inv.mu1 = 10)

fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]     0.20117972  6.920473   -13.792067    16.532333 0.286
##  [2,]    -3.98882121 13.190570   -43.891631     9.065042 0.348
##  [3,]     0.17442788  5.128045    -9.260313    10.267010 0.282
##  [4,]    -1.13850944  4.585463   -13.045164     4.488906 0.276
##  [5,]    -0.15484197  4.533380    -8.180444    10.249189 0.256
##  [6,]    -0.03074158  6.282936   -14.832899    15.504284 0.308
##  [7,]     0.55075729  5.977633    -9.412162    16.585197 0.282
##  [8,]     4.22828783 13.293880    -8.027037    45.654245 0.356
##  [9,]     0.48536245  6.617803    -9.142538    16.297567 0.298
## [10,]    -0.54331277 16.949724   -21.248630     9.829122 0.334
## [11,]    -2.01883982  8.870233   -27.357571     8.607479 0.312
## [12,]    -1.41256936  6.005920   -19.418836     6.594701 0.320
## [13,]    -1.54081159  5.745344   -16.976281     6.777589 0.306
## [14,]    -0.27200502  4.375811   -10.028084    10.075541 0.290
## [15,]    -0.87900623  5.050577   -12.279666     5.793930 0.276
## [16,]    -0.74731445  5.077872   -12.407591     9.017995 0.288
## [17,]    -6.89760808 14.776273   -54.172143     2.518153 0.422
## [18,]    -0.72376261  5.343980   -12.102634     9.470188 0.320
## [19,]    -0.71784886  4.489023   -11.583507     5.675548 0.250
## [20,]    -0.25308924  6.661631   -11.952993    13.177638 0.306
plot(fit.npb.24$beta[,1], type = "l")

plot(fit.npb.24$beta[,2], type = "l")

plot(fit.npb.24$beta[,13], type = "l")

4.2 Fit the NPB model

Below I’ve used the 24th set of priors and set scaleY = T

The priors are as follows: r priors.npb.24

Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure

priors.npb <- priors.npb.24

#' Exposures
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "pct_tree_cover"     
##  [4] "pct_impervious"      "mean_aadt_intensity" "dist_m_tri"         
##  [7] "dist_m_npl"          "dist_m_waste_site"   "dist_m_major_emit"  
## [10] "dist_m_cafo"         "dist_m_mine_well"    "cvd_rate_adj"       
## [13] "res_rate_adj"        "violent_crime_rate"  "property_crime_rate"
## [16] "pct_less_hs"         "pct_unemp"           "pct_limited_eng"    
## [19] "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
# fit.npb <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
#                scaleY = TRUE,
#                priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb, file = here::here("Results", "NPB_Birth_Weight_v3.1.rdata"))

load(here::here("Results", "NPB_Birth_Weight_v3.1.rdata"))
npb.sum <- summary(fit.npb)

4.2.1 First, main effect regression coefficients with PIPs

rownames(npb.sum$main.effects) <- colnames(X.scaled)
npb.sum$main.effects
##                     Posterior Mean        SD 95% CI Lower 95% CI Upper    PIP
## mean_pm                -0.39837259  5.706922   -14.272077    13.023276 0.2316
## mean_o3               -71.80706190 93.884623  -264.254977    12.372492 0.6048
## pct_tree_cover          0.03367814  6.086329   -13.793967    15.494484 0.2356
## pct_impervious         -1.34207610  5.910994   -18.462241     6.529494 0.2460
## mean_aadt_intensity     0.25489116  5.171531    -9.959488    13.922798 0.2220
## dist_m_tri             -0.31617476  5.423478   -13.572703    12.023496 0.2232
## dist_m_npl              0.34482520  5.632786   -10.088418    13.552340 0.2052
## dist_m_waste_site       3.61995576 11.756139    -6.346655    44.627720 0.2732
## dist_m_major_emit       0.70834014  5.967465    -8.596854    17.429979 0.2236
## dist_m_cafo            -2.19539809 16.092387   -32.777890    17.414786 0.2812
## dist_m_mine_well       -2.25982667  7.981283   -26.647074     6.947264 0.2840
## cvd_rate_adj           -1.65938278  7.117165   -21.911126     5.916137 0.2540
## res_rate_adj           -2.14263404  7.216720   -24.799903     5.059980 0.2716
## violent_crime_rate     -0.11310820  5.863106   -12.216716    13.045736 0.2180
## property_crime_rate    -1.05580099  5.655726   -15.784983     8.005556 0.2448
## pct_less_hs            -1.05396646  6.050934   -16.755494     6.638840 0.2364
## pct_unemp              -6.75999096 15.664698   -56.910641     2.691673 0.3736
## pct_limited_eng        -0.88182672  5.539078   -15.381236     8.522579 0.2276
## pct_hh_pov             -1.10915865  6.305950   -17.842206     7.134635 0.2376
## pct_poc                -0.20029315  6.599061   -14.007899    13.146894 0.2336
npb.sum$main.effects$exp <- rownames(npb.sum$main.effects)
## Warning in npb.sum$main.effects$exp <- rownames(npb.sum$main.effects): Coercing
## LHS to a list
write_csv(as.data.frame(npb.sum$main.effects), here::here("Results", "NPB_Main_Effects_Birth_Weight.csv"))

#' Which one's have PIPs > 0.5
# selected_exp <- which(npb.sum$main.effects[,"PIP"] >= 0.5)
# selected_exp

4.2.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum$interactions
##         Posterior Mean           SD 95% CI Lower 95% CI Upper    PIP
##   [1,]  -0.00852215445   0.37326203       0.0000       0.0000 0.0020
##   [2,]   0.01246066779   0.52231082       0.0000       0.0000 0.0036
##   [3,]  -0.00857544475   0.43086228       0.0000       0.0000 0.0024
##   [4,]   0.01200773299   0.43735746       0.0000       0.0000 0.0028
##   [5,]   0.02133322904   0.52229780       0.0000       0.0000 0.0024
##   [6,]  -0.00159817433   0.30823571       0.0000       0.0000 0.0024
##   [7,]  -0.00358887092   0.44827747       0.0000       0.0000 0.0036
##   [8,]  -0.01524024738   0.81409452       0.0000       0.0000 0.0016
##   [9,]  -0.02273428101   0.87219171       0.0000       0.0000 0.0012
##  [10,]  -0.01680612251   0.56706332       0.0000       0.0000 0.0012
##  [11,]   0.00069135071   0.03456754       0.0000       0.0000 0.0004
##  [12,]  -0.02026199314   0.59508189       0.0000       0.0000 0.0024
##  [13,]  -0.00390810510   0.22788632       0.0000       0.0000 0.0028
##  [14,]  -0.02534220377   0.54603620       0.0000       0.0000 0.0028
##  [15,]  -0.00226728366   0.31987735       0.0000       0.0000 0.0020
##  [16,]  -0.00370424994   0.30022571       0.0000       0.0000 0.0020
##  [17,]  -0.01013069933   0.50653497       0.0000       0.0000 0.0004
##  [18,]  -0.00732528715   0.48172079       0.0000       0.0000 0.0036
##  [19,]   0.00548247397   0.30748879       0.0000       0.0000 0.0012
##  [20,]  -0.00008835512   0.18914950       0.0000       0.0000 0.0020
##  [21,]   0.00422595015   0.21503826       0.0000       0.0000 0.0016
##  [22,]   0.00000000000   0.00000000       0.0000       0.0000 0.0000
##  [23,]  -0.04815352484   1.21713332       0.0000       0.0000 0.0032
##  [24,]  -0.00494479757   0.51132961       0.0000       0.0000 0.0008
##  [25,]  -0.07745324239   1.59860588       0.0000       0.0000 0.0040
##  [26,]   0.00366372004   0.18318600       0.0000       0.0000 0.0004
##  [27,]  -0.09553872222   1.83606876       0.0000       0.0000 0.0048
##  [28,]  -0.04064048904   0.81042860       0.0000       0.0000 0.0036
##  [29,]   0.01122095306   0.54117256       0.0000       0.0000 0.0016
##  [30,]  -0.00832011097   0.33120848       0.0000       0.0000 0.0012
##  [31,]   0.00606721021   0.42728042       0.0000       0.0000 0.0016
##  [32,]  -0.01062203310   0.28249997       0.0000       0.0000 0.0020
##  [33,]   0.01577733949   0.77172169       0.0000       0.0000 0.0024
##  [34,]   0.00799471556   0.32842418       0.0000       0.0000 0.0016
##  [35,]   0.00515382669   0.42805758       0.0000       0.0000 0.0016
##  [36,]   0.02864710521   0.66767430       0.0000       0.0000 0.0024
##  [37,]   0.01731419885   0.61579742       0.0000       0.0000 0.0016
##  [38,]  -0.00173809030   0.41739057       0.0000       0.0000 0.0024
##  [39,]  -0.00167930673   0.06972500       0.0000       0.0000 0.0008
##  [40,]  -0.00492535313   0.57678176       0.0000       0.0000 0.0020
##  [41,]   0.00154606481   0.27353512       0.0000       0.0000 0.0016
##  [42,]  -0.00549857939   0.24670602       0.0000       0.0000 0.0012
##  [43,]  -0.00284522459   0.22688334       0.0000       0.0000 0.0016
##  [44,]  -0.00018029778   0.08981227       0.0000       0.0000 0.0008
##  [45,]  -0.04519288653   1.16306458       0.0000       0.0000 0.0036
##  [46,]   0.00251325603   0.33176290       0.0000       0.0000 0.0020
##  [47,]   0.01042665769   0.97184859       0.0000       0.0000 0.0016
##  [48,]  -0.00454133566   0.43281952       0.0000       0.0000 0.0012
##  [49,]  -0.00136538119   0.23713005       0.0000       0.0000 0.0020
##  [50,]   0.02845914613   0.99514444       0.0000       0.0000 0.0032
##  [51,]   0.00377009273   0.58557318       0.0000       0.0000 0.0028
##  [52,]  -0.00117229336   0.15087522       0.0000       0.0000 0.0020
##  [53,]   0.02745358268   1.55278260       0.0000       0.0000 0.0012
##  [54,]   0.00018292834   0.51781716       0.0000       0.0000 0.0016
##  [55,]   0.02683886892   0.75962445       0.0000       0.0000 0.0028
##  [56,]   0.01104787691   0.30776526       0.0000       0.0000 0.0016
##  [57,]   0.00769422328   0.30978008       0.0000       0.0000 0.0020
##  [58,]   0.00085253830   0.15912355       0.0000       0.0000 0.0012
##  [59,]  -0.00218287344   0.24382162       0.0000       0.0000 0.0012
##  [60,]  -0.01543589463   0.40165840       0.0000       0.0000 0.0016
##  [61,]  -0.00190298316   0.39279964       0.0000       0.0000 0.0016
##  [62,]  -0.03456175599   0.98071853       0.0000       0.0000 0.0024
##  [63,]  -0.00497286976   0.42669993       0.0000       0.0000 0.0016
##  [64,]  -0.00697267127   0.24888352       0.0000       0.0000 0.0008
##  [65,]  -0.00090069986   0.13010671       0.0000       0.0000 0.0008
##  [66,]  -0.02094556083   0.65562805       0.0000       0.0000 0.0028
##  [67,]  -0.00703986218   0.43040297       0.0000       0.0000 0.0028
##  [68,]  -0.01079819042   0.33610501       0.0000       0.0000 0.0024
##  [69,]  -0.00750342536   0.56754814       0.0000       0.0000 0.0024
##  [70,]  -0.00768561923   0.39493432       0.0000       0.0000 0.0020
##  [71,]   0.01121509908   0.50105676       0.0000       0.0000 0.0008
##  [72,]  -0.00549804642   0.19772987       0.0000       0.0000 0.0008
##  [73,]   0.01221606673   0.50567497       0.0000       0.0000 0.0020
##  [74,]   0.01872320592   0.62381993       0.0000       0.0000 0.0024
##  [75,]  -0.03464296550   1.13745545       0.0000       0.0000 0.0024
##  [76,]   0.00013644190   0.08547686       0.0000       0.0000 0.0008
##  [77,]   0.01917552506   0.63784085       0.0000       0.0000 0.0032
##  [78,]  -0.05531680804   1.46487571       0.0000       0.0000 0.0040
##  [79,]  -0.01202215368   0.47988083       0.0000       0.0000 0.0020
##  [80,]   0.00000000000   0.00000000       0.0000       0.0000 0.0000
##  [81,]   0.00537523592   0.19463941       0.0000       0.0000 0.0008
##  [82,]  -0.02077005998   0.56343626       0.0000       0.0000 0.0016
##  [83,]  -0.00557922259   0.35925548       0.0000       0.0000 0.0012
##  [84,]   0.01623450019   0.90163612       0.0000       0.0000 0.0020
##  [85,]   0.01966246960   0.61116821       0.0000       0.0000 0.0040
##  [86,]  -0.00828375467   0.32672121       0.0000       0.0000 0.0024
##  [87,]   0.00228236590   0.11411829       0.0000       0.0000 0.0004
##  [88,]   0.00303697614   0.11792710       0.0000       0.0000 0.0012
##  [89,]   0.00242191722   0.43365521       0.0000       0.0000 0.0020
##  [90,]  -0.01905524252   0.61898933       0.0000       0.0000 0.0032
##  [91,]   0.00394362489   0.13901961       0.0000       0.0000 0.0012
##  [92,]   0.00558988907   0.35320987       0.0000       0.0000 0.0016
##  [93,]   0.00878887116   0.40125601       0.0000       0.0000 0.0020
##  [94,]  -0.00000720550   0.09267067       0.0000       0.0000 0.0020
##  [95,]   0.01228588443   0.38639282       0.0000       0.0000 0.0024
##  [96,]   0.03163911485   1.14069288       0.0000       0.0000 0.0028
##  [97,]   0.01457655907   0.54655230       0.0000       0.0000 0.0012
##  [98,]  -0.00443510568   0.38423333       0.0000       0.0000 0.0012
##  [99,]   0.00326456757   0.15933309       0.0000       0.0000 0.0020
## [100,]   0.00127230638   0.22733558       0.0000       0.0000 0.0016
## [101,]  -0.00140916970   0.15523224       0.0000       0.0000 0.0012
## [102,]   0.00643982195   0.27125777       0.0000       0.0000 0.0012
## [103,]   0.02420964913   0.86360078       0.0000       0.0000 0.0016
## [104,]   0.01369603824   0.72021888       0.0000       0.0000 0.0016
## [105,]  -0.00166766063   0.53854967       0.0000       0.0000 0.0020
## [106,]   0.00386888641   0.18236319       0.0000       0.0000 0.0016
## [107,]  -0.00189903735   0.37019759       0.0000       0.0000 0.0020
## [108,]  -0.01112835105   0.56733211       0.0000       0.0000 0.0024
## [109,]   0.00396817445   0.39898004       0.0000       0.0000 0.0028
## [110,]  -0.00090228096   0.20690373       0.0000       0.0000 0.0020
## [111,]  -0.00218832206   0.12233852       0.0000       0.0000 0.0008
## [112,]  -0.00609648982   0.24679902       0.0000       0.0000 0.0016
## [113,]   0.00353258476   0.39698491       0.0000       0.0000 0.0020
## [114,]   0.02505486899   0.72393851       0.0000       0.0000 0.0024
## [115,]  -0.00070311981   0.09033141       0.0000       0.0000 0.0016
## [116,]  -0.00802510137   0.43951100       0.0000       0.0000 0.0032
## [117,]  -0.00359706627   0.32345555       0.0000       0.0000 0.0012
## [118,]  -0.00047633753   0.09745806       0.0000       0.0000 0.0012
## [119,]   0.01589830891   0.61369794       0.0000       0.0000 0.0020
## [120,]   0.00175461395   0.19801324       0.0000       0.0000 0.0020
## [121,]  -0.00256587084   0.21778586       0.0000       0.0000 0.0024
## [122,]  -0.01256621299   0.44973833       0.0000       0.0000 0.0020
## [123,]   0.00909544491   0.32923598       0.0000       0.0000 0.0020
## [124,]  -0.00672977863   0.36267372       0.0000       0.0000 0.0016
## [125,]   0.02872118807   0.54180552       0.0000       0.0000 0.0036
## [126,]   0.05705217624   1.32722870       0.0000       0.0000 0.0036
## [127,]  -0.01099360266   0.31247391       0.0000       0.0000 0.0020
## [128,]  -0.02044534997   0.51597587       0.0000       0.0000 0.0016
## [129,]  -0.00089182438   0.31407478       0.0000       0.0000 0.0020
## [130,]  -0.00453843866   0.52112291       0.0000       0.0000 0.0020
## [131,]  -0.02633286065   0.60422570       0.0000       0.0000 0.0028
## [132,]  -0.01696692837   0.77029429       0.0000       0.0000 0.0008
## [133,]  -0.00329542430   0.25432066       0.0000       0.0000 0.0020
## [134,]   0.00362775462   0.18138773       0.0000       0.0000 0.0004
## [135,]  -0.00208307513   0.08948807       0.0000       0.0000 0.0008
## [136,]  -0.00515059462   0.32551050       0.0000       0.0000 0.0020
## [137,]  -0.00223403827   0.11170191       0.0000       0.0000 0.0004
## [138,]  -0.00083834907   0.31557377       0.0000       0.0000 0.0012
## [139,]  -0.00808394229   0.42920147       0.0000       0.0000 0.0020
## [140,]   0.00432192325   0.21609616       0.0000       0.0000 0.0004
## [141,]   0.00071166866   0.26829412       0.0000       0.0000 0.0012
## [142,]   0.00487547765   0.48717733       0.0000       0.0000 0.0016
## [143,]   0.00818539091   0.46973490       0.0000       0.0000 0.0028
## [144,]  -0.00236199577   0.08701391       0.0000       0.0000 0.0008
## [145,]   0.00127487904   0.06374395       0.0000       0.0000 0.0004
## [146,]   0.00204513133   0.30889869       0.0000       0.0000 0.0016
## [147,]   0.00228972989   0.08096896       0.0000       0.0000 0.0008
## [148,]   0.00007921453   0.21117862       0.0000       0.0000 0.0012
## [149,]   0.00033146525   0.34911117       0.0000       0.0000 0.0020
## [150,]   0.08023667097   2.25776385       0.0000       0.0000 0.0036
## [151,]   0.01274061284   0.44542978       0.0000       0.0000 0.0028
## [152,]   0.48635418770   6.27718645       0.0000       0.0000 0.0092
## [153,]   0.03624257490   1.01257218       0.0000       0.0000 0.0020
## [154,]   0.01860972492   0.63538108       0.0000       0.0000 0.0028
## [155,]   0.00441272417   0.37145545       0.0000       0.0000 0.0016
## [156,]   0.00200439089   0.60913640       0.0000       0.0000 0.0032
## [157,]  -0.00624758312   0.35718363       0.0000       0.0000 0.0020
## [158,]  -0.02007744076   0.90412429       0.0000       0.0000 0.0024
## [159,]  -0.09878237910   1.87735457       0.0000       0.0000 0.0060
## [160,]  -0.01127670689   0.51935682       0.0000       0.0000 0.0024
## [161,]  -0.02036518250   0.71591700       0.0000       0.0000 0.0028
## [162,]  -0.00038953861   0.23861213       0.0000       0.0000 0.0012
## [163,]  -0.01155584508   0.38185272       0.0000       0.0000 0.0012
## [164,]  -0.02332636410   0.73256265       0.0000       0.0000 0.0024
## [165,]  -0.00924186005   0.35425415       0.0000       0.0000 0.0012
## [166,]  -0.00149688244   0.43776938       0.0000       0.0000 0.0028
## [167,]  -0.00518939293   0.35794433       0.0000       0.0000 0.0020
## [168,]   0.00144077196   0.39340332       0.0000       0.0000 0.0012
## [169,]  -0.00108037151   0.05401858       0.0000       0.0000 0.0004
## [170,]  -0.00021128259   0.01056413       0.0000       0.0000 0.0004
## [171,]   0.02165929850   0.52353615       0.0000       0.0000 0.0020
## [172,]   0.00745208905   0.32868698       0.0000       0.0000 0.0008
## [173,]   0.00365683116   0.18284156       0.0000       0.0000 0.0004
## [174,]   0.00644806254   0.33176913       0.0000       0.0000 0.0028
## [175,]   0.00258451237   0.27275095       0.0000       0.0000 0.0012
## [176,]  -0.00857669160   0.29088691       0.0000       0.0000 0.0020
## [177,]  -0.00508504731   0.18808237       0.0000       0.0000 0.0008
## [178,]  -0.01030383702   0.24493363       0.0000       0.0000 0.0020
## [179,]  -0.01370044520   0.49512298       0.0000       0.0000 0.0016
## [180,]   0.01002365944   0.35732017       0.0000       0.0000 0.0012
## [181,]  -0.00627522147   0.26411584       0.0000       0.0000 0.0024
## [182,]  -0.00133873228   0.33302200       0.0000       0.0000 0.0020
## [183,]  -0.00459098448   0.16257991       0.0000       0.0000 0.0008
## [184,]   0.00813744505   0.38409760       0.0000       0.0000 0.0020
## [185,]  -0.02406873307   0.76949329       0.0000       0.0000 0.0016
## [186,]  -0.00173071716   0.18033813       0.0000       0.0000 0.0008
## [187,]  -0.01246315717   0.47832730       0.0000       0.0000 0.0020
## [188,]   0.00584521355   0.29226068       0.0000       0.0000 0.0004
## [189,]   0.00110323877   0.05516194       0.0000       0.0000 0.0004
## [190,]  -0.00566012092   0.36672144       0.0000       0.0000 0.0024
## [191,]   0.01054697738   0.27345043       0.0000       0.0000 0.0020
## [192,]   0.00147705081   0.52822842       0.0000       0.0000 0.0020
## [193,]  -0.00257253991   0.12659485       0.0000       0.0000 0.0008
## [194,]   0.00051320444   0.39286732       0.0000       0.0000 0.0024
## [195,]  -0.01110342949   0.65331263       0.0000       0.0000 0.0016
## [196,]  -0.01591545652   1.29781775       0.0000       0.0000 0.0044
## [197,]   0.00423485777   0.89480136       0.0000       0.0000 0.0032
## [198,]  -0.03470526766   1.17953362       0.0000       0.0000 0.0020
## [199,]  -0.02717077882   0.95709076       0.0000       0.0000 0.0020
## [200,]  -0.00528525068   0.65211168       0.0000       0.0000 0.0024
## [201,]  -0.04520710586   4.61697716       0.0000       0.0000 0.0036
## [202,]  -0.10312305242   2.93845398       0.0000       0.0000 0.0028
## [203,]  -0.00037663661   0.22448844       0.0000       0.0000 0.0020
## [204,]   0.00644439996   0.24042372       0.0000       0.0000 0.0008
## [205,]  -0.00469327435   0.23731415       0.0000       0.0000 0.0016
## [206,]  -0.00334856693   0.62163885       0.0000       0.0000 0.0020
## [207,]  -0.00088703025   0.04435151       0.0000       0.0000 0.0004
## [208,]   0.03549355546   1.13441264       0.0000       0.0000 0.0036
## [209,]   0.09501064236   3.82439749       0.0000       0.0000 0.0028
## [210,]  -0.07050803971   2.10560691       0.0000       0.0000 0.0040
## [211,]  -0.00288822347   0.21006806       0.0000       0.0000 0.0016
## [212,]  -0.02443416150   0.98734153       0.0000       0.0000 0.0024
## [213,]  -0.00943251756   0.63666572       0.0000       0.0000 0.0048
## [214,]   0.03138404001   1.02451722       0.0000       0.0000 0.0020
## [215,]  -0.00566292527   0.23730037       0.0000       0.0000 0.0016
## [216,]  -0.01686541634   0.51025719       0.0000       0.0000 0.0020
## [217,]   0.02987496549   0.83518964       0.0000       0.0000 0.0036
## [218,]  -0.01324106498   0.50754803       0.0000       0.0000 0.0020
## [219,]  -0.00770513716   0.31815580       0.0000       0.0000 0.0008
## [220,]  -0.01697734631   0.82116803       0.0000       0.0000 0.0024
## [221,]  -0.01501111830   0.65851288       0.0000       0.0000 0.0032
## [222,]   0.00088630364   1.74607982       0.0000       0.0000 0.0032
## [223,]  -0.04943703727   1.62428803       0.0000       0.0000 0.0028
## [224,]   0.00049131213   0.69786919       0.0000       0.0000 0.0028
## [225,]   0.00036591234   0.01829562       0.0000       0.0000 0.0004
## [226,]  -0.00473096874   0.41203087       0.0000       0.0000 0.0028
## [227,]   0.17704189933   8.71097437       0.0000       0.0000 0.0032
## [228,]  -0.01346919922   0.40447612       0.0000       0.0000 0.0016
## [229,]  -0.00555869850   0.33432634       0.0000       0.0000 0.0016
## [230,] -80.57086597144 109.27564315    -291.9708       0.0000 0.3740
## [231,]  57.27519005883 127.94463070       0.0000     389.1348 0.1748
## [232,] 124.91135602763 155.75340087       0.0000     404.2391 0.4172
## [233,]  -0.00785085233   0.50457381       0.0000       0.0000 0.0016
## [234,]  -0.24219905854   5.01765093       0.0000       0.0000 0.0044
## [235,]  -0.01073074892   0.64239507       0.0000       0.0000 0.0020
## [236,]  -0.00570466500   0.28523325       0.0000       0.0000 0.0004
## [237,]   0.00315860336   0.34609240       0.0000       0.0000 0.0008
## [238,]  -0.03875290388   2.04307162       0.0000       0.0000 0.0032
## [239,]  -0.18829285782   4.00008807       0.0000       0.0000 0.0040
## [240,]   0.02254961213   0.56312197       0.0000       0.0000 0.0024
## [241,]   0.00839228796   0.45798175       0.0000       0.0000 0.0032
## [242,]   0.00249501431   0.19433804       0.0000       0.0000 0.0020
## [243,]   0.00356116246   0.20751844       0.0000       0.0000 0.0012
## [244,]   0.00732411277   0.28627723       0.0000       0.0000 0.0016
## [245,]  -0.02642363895   1.21576207       0.0000       0.0000 0.0016
## [246,]   0.00158718241   0.41436807       0.0000       0.0000 0.0020
## [247,]   0.05205737964   2.09950797       0.0000       0.0000 0.0032
## [248,]   0.01617139562   1.23519449       0.0000       0.0000 0.0020
## [249,]   0.07082814296   2.61623158       0.0000       0.0000 0.0044
## [250,]  -0.00914436026   0.43872592       0.0000       0.0000 0.0020
## [251,]   0.02302741445   1.10300228       0.0000       0.0000 0.0012
## [252,]   0.00000000000   0.00000000       0.0000       0.0000 0.0000
## [253,]  -0.04843671450   2.16513993       0.0000       0.0000 0.0036
## [254,]  -0.00812745276   0.87380135       0.0000       0.0000 0.0024
## [255,]  -0.00564824780   0.66354197       0.0000       0.0000 0.0024
## [256,]  -0.00235946711   0.08316208       0.0000       0.0000 0.0012
## [257,]   0.00292900825   0.18644215       0.0000       0.0000 0.0008
## [258,]   0.00565870283   0.64804178       0.0000       0.0000 0.0016
## [259,]   0.02077007732   1.25275510       0.0000       0.0000 0.0016
## [260,]   0.05554589025   1.66647915       0.0000       0.0000 0.0020
## [261,]   0.00366028615   0.19942057       0.0000       0.0000 0.0016
## [262,]  -0.00718782413   0.47642795       0.0000       0.0000 0.0024
## [263,]   0.00609642660   0.27784404       0.0000       0.0000 0.0024
## [264,]   0.01624147309   0.73583013       0.0000       0.0000 0.0028
## [265,]  -0.00054140412   0.30623676       0.0000       0.0000 0.0024
## [266,]   0.00143103248   0.11081136       0.0000       0.0000 0.0012
## [267,]  -0.00289903633   0.10481107       0.0000       0.0000 0.0008
## [268,]   0.02494657862   0.73793799       0.0000       0.0000 0.0028
## [269,]  -0.00280072945   0.44178856       0.0000       0.0000 0.0016
## [270,]  -0.01453088353   0.53178109       0.0000       0.0000 0.0012
## [271,]   0.00665094529   0.17645090       0.0000       0.0000 0.0020
## [272,]  -0.01674275578   0.57001499       0.0000       0.0000 0.0028
## [273,]   0.02304435466   1.84671842       0.0000       0.0000 0.0024
## [274,]   0.00880316707   0.36555884       0.0000       0.0000 0.0024
## [275,]   0.07014267312   2.42580730       0.0000       0.0000 0.0020
## [276,]  -0.00016821970   0.02408931       0.0000       0.0000 0.0008
## [277,]  -0.01679801286   1.03882692       0.0000       0.0000 0.0020
## [278,]  -0.00918228240   0.37227404       0.0000       0.0000 0.0028
## [279,]  -0.12150064619   5.69682879       0.0000       0.0000 0.0020
## [280,]  -0.02044003023   0.60412950       0.0000       0.0000 0.0020
## [281,]   0.00532951745   0.61186914       0.0000       0.0000 0.0020
## [282,]  -0.01380893739   0.60192914       0.0000       0.0000 0.0020
## [283,]  -0.03490050770   1.01141168       0.0000       0.0000 0.0028
## [284,]   0.01510218653   1.21586032       0.0000       0.0000 0.0024
## [285,]  -0.00734950694   0.32881624       0.0000       0.0000 0.0016
## [286,]  -0.00527103385   0.71497728       0.0000       0.0000 0.0044
## [287,]   0.01284910951   0.58218622       0.0000       0.0000 0.0008
## [288,]  -0.00665398912   0.52684034       0.0000       0.0000 0.0016
## [289,]  -0.00382600971   0.52714024       0.0000       0.0000 0.0032
## [290,]  -0.01765980962   0.95253472       0.0000       0.0000 0.0024
## [291,]  -0.00632745985   0.24390607       0.0000       0.0000 0.0020
## [292,]  -0.03468579196   0.83465838       0.0000       0.0000 0.0028
## [293,]  -0.00618871743   0.50112940       0.0000       0.0000 0.0024
## [294,]  -0.05908363394   1.62544184       0.0000       0.0000 0.0040
## [295,]  -0.01217544056   0.49043409       0.0000       0.0000 0.0020
## [296,]   0.01028885408   0.47286943       0.0000       0.0000 0.0020
## [297,]  -0.02666412560   0.72006901       0.0000       0.0000 0.0024
## [298,]   0.00684575539   0.98848002       0.0000       0.0000 0.0036
## [299,]  -0.00963737122   0.40902418       0.0000       0.0000 0.0024
## [300,]  -0.01166223149   1.39299695       0.0000       0.0000 0.0020
## [301,]   0.17920638930   3.82236803       0.0000       0.0000 0.0048
## [302,]   0.00331563630   0.31619410       0.0000       0.0000 0.0012
## [303,]  -0.01171285648   0.75148842       0.0000       0.0000 0.0016
## [304,]  -0.01078203199   1.12288148       0.0000       0.0000 0.0028
## [305,]   0.04203003327   1.92727284       0.0000       0.0000 0.0024
## [306,]  -0.04165689962   1.10623611       0.0000       0.0000 0.0024
## [307,]   0.05106917882   2.13068956       0.0000       0.0000 0.0032
## [308,]  -0.01639922517   0.47251083       0.0000       0.0000 0.0024
## [309,]   0.01527367553   0.54993752       0.0000       0.0000 0.0020
## [310,]   0.00260509305   0.31455629       0.0000       0.0000 0.0012
## [311,]   0.02406283417   1.02205542       0.0000       0.0000 0.0048
## [312,]   0.03115747301   2.08252894       0.0000       0.0000 0.0024
## [313,]  -0.02555461548   1.28112297       0.0000       0.0000 0.0020
## [314,]   0.01476038989   0.41625053       0.0000       0.0000 0.0016
## [315,]  -0.05658161157   1.30232519       0.0000       0.0000 0.0032
## [316,]  -0.00601750569   0.83208762       0.0000       0.0000 0.0012
## [317,]  -0.03477571345   0.97663406       0.0000       0.0000 0.0044
## [318,]  -0.01040531969   0.46913984       0.0000       0.0000 0.0016
## [319,]   0.00285990988   0.38620718       0.0000       0.0000 0.0020
## [320,]  -0.00197188178   0.08865738       0.0000       0.0000 0.0008
## [321,]  -0.00704890119   0.46577519       0.0000       0.0000 0.0020
## [322,]  -0.00743600197   0.25812415       0.0000       0.0000 0.0012
## [323,]  -0.00220620756   0.47717830       0.0000       0.0000 0.0020
## [324,]   0.12322182592   3.58201430       0.0000       0.0000 0.0028
## [325,]  -0.00310911665   0.15545583       0.0000       0.0000 0.0004
## [326,]  -0.02097871760   0.70632518       0.0000       0.0000 0.0036
## [327,]   0.28893540039   6.67591298       0.0000       0.0000 0.0040
## [328,]  -0.00941931120   0.69748880       0.0000       0.0000 0.0016
## [329,]   0.00267191679   0.57378689       0.0000       0.0000 0.0012
## [330,]   0.01169009708   0.60091601       0.0000       0.0000 0.0020
## [331,]  -0.00791760994   0.52253478       0.0000       0.0000 0.0036
## [332,]  -0.00040163541   0.09282016       0.0000       0.0000 0.0016
## [333,]   0.00772266744   0.47391815       0.0000       0.0000 0.0020
## [334,]   0.00386195562   0.38341248       0.0000       0.0000 0.0020
## [335,]  -0.01005763017   0.53603341       0.0000       0.0000 0.0024
## [336,]   0.10827689675   2.37405973       0.0000       0.0000 0.0040
## [337,]   0.04342075131   1.62706574       0.0000       0.0000 0.0024
## [338,]   0.00423349606   0.15378655       0.0000       0.0000 0.0008
## [339,]  -0.03593124008   1.13984243       0.0000       0.0000 0.0032
## [340,]   0.03096697643   1.41443355       0.0000       0.0000 0.0020
## [341,]   0.00582644207   0.25369707       0.0000       0.0000 0.0016
## [342,]  -0.01838919919   0.55266647       0.0000       0.0000 0.0028
## [343,]  -0.04045665251   1.15777371       0.0000       0.0000 0.0036
## [344,]  -0.00786885568   0.56900140       0.0000       0.0000 0.0020
## [345,]  -0.00925973757   0.49926367       0.0000       0.0000 0.0040
## [346,]   0.00019237478   0.43627328       0.0000       0.0000 0.0016
## [347,]   0.00795874605   0.34925281       0.0000       0.0000 0.0012
## [348,]   0.00328084233   0.13518636       0.0000       0.0000 0.0008
## [349,]   0.00051612872   0.16295403       0.0000       0.0000 0.0016
## [350,]   0.01438505804   0.53700766       0.0000       0.0000 0.0028
## [351,]  -0.02365149423   0.89979825       0.0000       0.0000 0.0012
## [352,]   0.07299083574   3.50986456       0.0000       0.0000 0.0028
## [353,]   0.00642677038   1.29192451       0.0000       0.0000 0.0040
## [354,]  -0.02572126900   0.65313640       0.0000       0.0000 0.0028
## [355,]  -0.02295225790   0.82708974       0.0000       0.0000 0.0020
## [356,]  -0.01499651767   0.87551829       0.0000       0.0000 0.0020
## [357,]  -0.15324359524   7.03761913       0.0000       0.0000 0.0052
## [358,]  -0.00134452162   0.17622330       0.0000       0.0000 0.0008
## [359,]  -0.02168153618   0.83135223       0.0000       0.0000 0.0012
## [360,]  -0.00586989567   0.53053282       0.0000       0.0000 0.0024
## [361,]   0.01139656149   0.51714996       0.0000       0.0000 0.0008
## [362,]  -0.02284053537   0.65916992       0.0000       0.0000 0.0028
## [363,]   0.00675758962   0.72302838       0.0000       0.0000 0.0028
## [364,]   0.00055002434   0.14527514       0.0000       0.0000 0.0008
## [365,]  -0.01059349751   0.59539381       0.0000       0.0000 0.0020
## [366,]   0.02266163449   1.19100462       0.0000       0.0000 0.0024
## [367,]   0.01325376029   0.40928891       0.0000       0.0000 0.0020
## [368,]  -0.00125723553   0.08320120       0.0000       0.0000 0.0008
## [369,]  -0.08069095838   2.78307756       0.0000       0.0000 0.0032
## [370,]  -0.00230672409   0.13488569       0.0000       0.0000 0.0008
## [371,]  -0.02726939033   0.83112218       0.0000       0.0000 0.0024
## [372,]   0.01076777859   0.37370517       0.0000       0.0000 0.0012
## [373,]  -0.00224800261   0.27663975       0.0000       0.0000 0.0008
## [374,]  -0.03628444860   1.47095945       0.0000       0.0000 0.0040
## [375,]   0.00761725568   0.44070788       0.0000       0.0000 0.0032
## [376,]   0.00755286315   0.41005796       0.0000       0.0000 0.0020
## [377,]  -0.01324696605   0.66353505       0.0000       0.0000 0.0032
## [378,]   0.36454314503   7.60369643       0.0000       0.0000 0.0040
## [379,]   0.00214770579   0.31450580       0.0000       0.0000 0.0016
## [380,]   0.00221200438   0.75585046       0.0000       0.0000 0.0012
## [381,]  -0.03359844898   1.67992245       0.0000       0.0000 0.0004
## [382,]   0.12867218623   3.79471753       0.0000       0.0000 0.0020
## [383,]  -0.08947480663   3.71287222       0.0000       0.0000 0.0028
## [384,]   0.01316312218   0.84002957       0.0000       0.0000 0.0040
## [385,]  -0.00203378492   0.10168925       0.0000       0.0000 0.0004
## [386,]   0.03043205300   1.12285194       0.0000       0.0000 0.0028
## [387,]   0.02206677724   1.04920207       0.0000       0.0000 0.0008
## [388,]   0.00989636154   0.32994790       0.0000       0.0000 0.0012
## [389,]   0.00229651286   0.27556941       0.0000       0.0000 0.0028
## [390,]   0.05661901784   2.05127203       0.0000       0.0000 0.0036
## [391,]  -0.08308939807   2.00392544       0.0000       0.0000 0.0036
## [392,]   0.03487154175   1.44194808       0.0000       0.0000 0.0012
## [393,]  -0.00871702562   0.30677711       0.0000       0.0000 0.0012
## [394,]  -0.00005989636   0.30690102       0.0000       0.0000 0.0008
## [395,]  -0.02256740553   1.12679621       0.0000       0.0000 0.0016
## [396,]  -0.00474628023   0.25766252       0.0000       0.0000 0.0024
## [397,]  -0.00439168519   0.39282785       0.0000       0.0000 0.0024
## [398,]   0.00123283458   0.39320376       0.0000       0.0000 0.0016
## [399,]  -0.02124924507   0.68529269       0.0000       0.0000 0.0020
## [400,]  -0.00554183726   0.38883495       0.0000       0.0000 0.0012
## [401,]   0.01139633920   0.39926031       0.0000       0.0000 0.0016
## [402,]  -0.00581231603   0.29620450       0.0000       0.0000 0.0020
## [403,]   0.02542174216   1.22911935       0.0000       0.0000 0.0016
## [404,]   0.02732727095   1.08862475       0.0000       0.0000 0.0016
## [405,]   0.07190168859   2.35691843       0.0000       0.0000 0.0032
## [406,]   0.01160528196   1.35025360       0.0000       0.0000 0.0044
## [407,]   0.00418372710   0.47386627       0.0000       0.0000 0.0016
## [408,]  -0.01421251849   1.50926567       0.0000       0.0000 0.0020
## [409,]   0.33545522497   8.87821214       0.0000       0.0000 0.0044
## [410,]   0.03260186738   1.06376281       0.0000       0.0000 0.0016
## [411,]  -0.00574585121   0.44749868       0.0000       0.0000 0.0008
## [412,]  -0.01856690657   1.01610652       0.0000       0.0000 0.0020
## [413,]   0.03001706590   2.57260497       0.0000       0.0000 0.0028
## [414,]   0.00336833924   0.77821038       0.0000       0.0000 0.0024
## [415,]   0.00135742806   0.47347698       0.0000       0.0000 0.0028
## [416,]   0.00263092300   0.17694727       0.0000       0.0000 0.0012
## [417,]  -0.00825738304   1.02250075       0.0000       0.0000 0.0032
## [418,]  -0.00444516897   0.42363555       0.0000       0.0000 0.0020
## [419,]  -0.02161897271   0.70568330       0.0000       0.0000 0.0028
## [420,]  -0.00614655743   0.28570930       0.0000       0.0000 0.0020
## [421,]  -0.09499243984   2.69912603       0.0000       0.0000 0.0020
## [422,]   0.00492222653   0.38200994       0.0000       0.0000 0.0020
## [423,]  -0.00095279494   0.21935324       0.0000       0.0000 0.0012
## [424,]   0.00818676623   0.48858238       0.0000       0.0000 0.0012
## [425,]   0.01017174057   0.20993447       0.0000       0.0000 0.0032
## [426,]  -0.00808892200   0.29849882       0.0000       0.0000 0.0020
## [427,]   0.00409101536   0.27096069       0.0000       0.0000 0.0016
## [428,]  -0.00697204351   0.37160749       0.0000       0.0000 0.0020
## [429,]  -0.00348310906   0.63809674       0.0000       0.0000 0.0016
## [430,]  -0.04268759771   2.29063200       0.0000       0.0000 0.0024
## [431,]   0.15200891484   4.82572724       0.0000       0.0000 0.0040
## [432,]  -0.06262232785   2.57587759       0.0000       0.0000 0.0028
## [433,]  -0.00220356584   0.18425421       0.0000       0.0000 0.0016
## [434,]  -0.00913081846   0.57074506       0.0000       0.0000 0.0020
## [435,]  -0.53084756842  10.48339786       0.0000       0.0000 0.0056
## [436,]  -0.05226763713   1.94968075       0.0000       0.0000 0.0012
## [437,]  -0.00088341842   0.47718867       0.0000       0.0000 0.0028
## [438,]  -0.01660695520   0.55177322       0.0000       0.0000 0.0028
## [439,]   0.00165433872   0.34782480       0.0000       0.0000 0.0024
## [440,]   0.01504540018   0.53397376       0.0000       0.0000 0.0016
## [441,]   0.01510946344   0.92538117       0.0000       0.0000 0.0016
## [442,]   0.28115521526   5.75197943       0.0000       0.0000 0.0044
## [443,]  -0.10121663231   3.04861888       0.0000       0.0000 0.0032
## [444,]  -0.03593894892   1.44592384       0.0000       0.0000 0.0020
## [445,]   0.00744217607   0.57007478       0.0000       0.0000 0.0028
## [446,]   0.07163958659   3.32840406       0.0000       0.0000 0.0024
## [447,]  -0.24975420383   5.33845645       0.0000       0.0000 0.0048
## [448,]  -0.00238503561   0.51989838       0.0000       0.0000 0.0028
## [449,]   0.01091058788   0.33718577       0.0000       0.0000 0.0012
## [450,]  -0.01731530030   0.53859206       0.0000       0.0000 0.0024
## [451,]   0.01222240047   0.53860137       0.0000       0.0000 0.0036
## [452,]   0.01699283696   0.84964185       0.0000       0.0000 0.0004
## [453,]  -0.02062891911   0.79903736       0.0000       0.0000 0.0024
## [454,]  -0.06486002924   1.70061848       0.0000       0.0000 0.0040
## [455,]   0.00839217602   0.30085491       0.0000       0.0000 0.0028
## [456,]  -0.00524258596   0.80406025       0.0000       0.0000 0.0020
## [457,]   0.02165282026   1.65152374       0.0000       0.0000 0.0020
## [458,]  -0.08157557851   2.19922409       0.0000       0.0000 0.0040
## [459,]  -0.00685869122   1.03089520       0.0000       0.0000 0.0020
## [460,]   0.00191390339   0.22238783       0.0000       0.0000 0.0012
## [461,]  -0.24160503538   6.82840233       0.0000       0.0000 0.0028
## [462,]  -0.00793111062   0.92790389       0.0000       0.0000 0.0016
## [463,]   0.01343902064   1.20769167       0.0000       0.0000 0.0024
## [464,]   0.02997841612   1.11843710       0.0000       0.0000 0.0028
## [465,]  -0.01588597320   0.81503974       0.0000       0.0000 0.0020
## [466,]  -0.01733332620   0.90380469       0.0000       0.0000 0.0020
## [467,]  -0.03151809183   0.95278664       0.0000       0.0000 0.0028
## [468,]   0.18123146259   3.76412841       0.0000       0.0000 0.0036
## [469,]  -1.00271810461  10.26862030       0.0000       0.0000 0.0152
## [470,]  -0.00147126480   0.26419375       0.0000       0.0000 0.0012
## [471,]   0.01300335519   0.33960802       0.0000       0.0000 0.0020
## [472,]   0.01790113539   1.34167104       0.0000       0.0000 0.0020
## [473,]  -0.12612078907   2.81192309       0.0000       0.0000 0.0064
## [474,]  -0.00158471030   0.60752935       0.0000       0.0000 0.0028
## [475,]   0.00479955972   0.50455867       0.0000       0.0000 0.0020
## [476,]  -0.05210590535   1.79867264       0.0000       0.0000 0.0032
## [477,]  -0.00285499563   0.34820573       0.0000       0.0000 0.0008
## [478,]  -0.01880459245   0.47814807       0.0000       0.0000 0.0016
## [479,]  -0.00277642851   0.34923947       0.0000       0.0000 0.0016
## [480,]   0.00235292692   1.45839801       0.0000       0.0000 0.0040
## [481,]   0.00592634636   0.64987753       0.0000       0.0000 0.0024
## [482,]  -0.03971926582   1.91705392       0.0000       0.0000 0.0012
## [483,]  -0.00516970403   0.23699091       0.0000       0.0000 0.0028
## [484,]  -0.00952048696   0.35051548       0.0000       0.0000 0.0008
## [485,]   0.02539539528   1.08256783       0.0000       0.0000 0.0020
## [486,]  -0.01055554549   0.31180292       0.0000       0.0000 0.0024
## [487,]  -0.08061217310   4.22675586       0.0000       0.0000 0.0032
## [488,]  -0.02602935901   0.95307122       0.0000       0.0000 0.0028
## [489,]  -0.00633005229   0.26819233       0.0000       0.0000 0.0016
## [490,]  -0.03653785534   0.92072242       0.0000       0.0000 0.0020
## [491,]   0.00248084877   0.11756501       0.0000       0.0000 0.0016
## [492,]  -0.05505683843   1.30485683       0.0000       0.0000 0.0028
## [493,]  -0.09738006783   2.38113420       0.0000       0.0000 0.0048
## [494,]  -0.04139661398   1.44626878       0.0000       0.0000 0.0012
## [495,]   0.40542053660   6.55260172       0.0000       0.0000 0.0080
## [496,]  -0.00270024686   0.45912977       0.0000       0.0000 0.0028
## [497,]   0.01088310630   0.39905062       0.0000       0.0000 0.0012
## [498,]  -0.00332540992   0.16627050       0.0000       0.0000 0.0004
## [499,]  -0.00953432103   0.47407592       0.0000       0.0000 0.0036
## [500,]  -0.00740801044   0.36500678       0.0000       0.0000 0.0020
## [501,]   0.01266314889   0.54877968       0.0000       0.0000 0.0028
## [502,]  -0.00441297593   0.42803129       0.0000       0.0000 0.0020
## [503,]   0.00013025606   0.78475696       0.0000       0.0000 0.0020
## [504,]   0.01123953747   0.43769653       0.0000       0.0000 0.0020
## [505,]  -0.01358243288   0.47658898       0.0000       0.0000 0.0012
## [506,]   0.00508684281   0.33607881       0.0000       0.0000 0.0024
## [507,]  -0.03342828258   1.25475025       0.0000       0.0000 0.0032
## [508,]  -0.06823000268   2.28717118       0.0000       0.0000 0.0036
## [509,]  -0.02097022568   1.21878654       0.0000       0.0000 0.0028
## [510,]  -0.01246441894   0.44992288       0.0000       0.0000 0.0024
## [511,]   0.02467337336   1.02672469       0.0000       0.0000 0.0016
## [512,]  -0.13338092010   2.98814944       0.0000       0.0000 0.0060
## [513,]  -0.43988693178   9.68851849       0.0000       0.0000 0.0052
## [514,]   0.01230695546   0.47344428       0.0000       0.0000 0.0020
## [515,]   0.00189623197   0.20296106       0.0000       0.0000 0.0008
## [516,]  -0.00726062538   0.75545796       0.0000       0.0000 0.0020
## [517,]  -0.00009657501   0.12560949       0.0000       0.0000 0.0008
## [518,]  -0.01584360517   0.60620399       0.0000       0.0000 0.0020
## [519,]  -0.09054652869   2.21569798       0.0000       0.0000 0.0044
## [520,]  -0.00013379573   0.43010905       0.0000       0.0000 0.0008
## [521,]   0.04778975983   2.49164151       0.0000       0.0000 0.0032
## [522,]  -0.01143112006   0.66837675       0.0000       0.0000 0.0028
## [523,]   0.00609702023   0.22984189       0.0000       0.0000 0.0016
## [524,]  -0.07012088478   2.60524269       0.0000       0.0000 0.0020
## [525,]  -0.01601623452   0.48908110       0.0000       0.0000 0.0020
## [526,]  -0.00755247119   0.38825984       0.0000       0.0000 0.0012
## [527,]   0.00002286726   0.07722196       0.0000       0.0000 0.0008
## [528,]  -0.01217474724   0.53778430       0.0000       0.0000 0.0008
## [529,]   0.00108589184   0.28014831       0.0000       0.0000 0.0016
## [530,]  -0.00873790197   0.43689510       0.0000       0.0000 0.0004
## [531,]  -0.00307837410   0.25535239       0.0000       0.0000 0.0008
## [532,]   0.06205131368   2.53176787       0.0000       0.0000 0.0036
## [533,]  -0.09782956292   2.88588625       0.0000       0.0000 0.0020
## [534,]   1.16296354539  17.46027909       0.0000       0.0000 0.0052
## [535,]   0.06953351964   2.33408751       0.0000       0.0000 0.0032
## [536,]  -0.00644790071   0.55045517       0.0000       0.0000 0.0032
## [537,]   0.02158326299   1.93205020       0.0000       0.0000 0.0028
## [538,]  -0.02575887531   1.01634298       0.0000       0.0000 0.0020
## [539,]  -1.82071780463  20.13004301       0.0000       0.0000 0.0124
## [540,]  -0.03452913874   1.01239498       0.0000       0.0000 0.0020
## [541,]   0.00121151030   0.21456211       0.0000       0.0000 0.0012
## [542,]  -0.00166730056   0.66008269       0.0000       0.0000 0.0012
## [543,]  -0.00816993466   0.33420172       0.0000       0.0000 0.0028
## [544,]  -0.01186073995   0.57366732       0.0000       0.0000 0.0020
## [545,]   0.01440445153   1.21801018       0.0000       0.0000 0.0012
## [546,]  -0.04070655683   1.18995656       0.0000       0.0000 0.0024
## [547,]   0.01287749739   0.38607706       0.0000       0.0000 0.0032
## [548,]  -0.00721886346   0.50262145       0.0000       0.0000 0.0012
## [549,]  -0.00433024596   0.37129593       0.0000       0.0000 0.0008
## [550,]  -0.22628630639   7.56847936       0.0000       0.0000 0.0036
## [551,]  -0.01313003569   0.45433522       0.0000       0.0000 0.0024
## [552,]  -0.06157759643   1.18165391       0.0000       0.0000 0.0040
## [553,]  -0.01446520906   0.67980157       0.0000       0.0000 0.0036
## [554,]  -0.00038724275   0.31241357       0.0000       0.0000 0.0012
## [555,]  -0.00509074184   0.31022597       0.0000       0.0000 0.0024
## [556,]  -0.00767730976   0.50070224       0.0000       0.0000 0.0016
## [557,]  -0.00656778043   0.33845419       0.0000       0.0000 0.0024
## [558,]   0.09848988616   2.77136150       0.0000       0.0000 0.0024
## [559,]  -0.02601094155   1.21800056       0.0000       0.0000 0.0040
## [560,]   0.54117124413  17.55649193       0.0000       0.0000 0.0040
## [561,]   0.07547497010   7.28315778       0.0000       0.0000 0.0036
## [562,]   0.02435091428   1.19127368       0.0000       0.0000 0.0016
## [563,]   0.00390352007   0.30656046       0.0000       0.0000 0.0016
## [564,]  -0.01488439371   0.57806909       0.0000       0.0000 0.0028
## [565,]  -1.31681660846  16.37597165       0.0000       0.0000 0.0088
## [566,]  -0.04937506023   1.47768634       0.0000       0.0000 0.0028
## [567,]   0.00381497262   0.25815509       0.0000       0.0000 0.0012
## [568,]  -0.00102498128   0.42249239       0.0000       0.0000 0.0016
## [569,]   0.00480004781   0.28234565       0.0000       0.0000 0.0016
## [570,]  -0.00578670927   0.88700902       0.0000       0.0000 0.0016
## [571,]  -0.00371617669   0.31053267       0.0000       0.0000 0.0016
## [572,]  -0.00044400820   0.06270389       0.0000       0.0000 0.0008
## [573,]  -0.00361417580   0.34668400       0.0000       0.0000 0.0024
## [574,]   0.00654328505   0.47385979       0.0000       0.0000 0.0012
## [575,]   0.00567159980   0.28273639       0.0000       0.0000 0.0032
## [576,]  -0.01032587620   0.65213816       0.0000       0.0000 0.0012
## [577,]   0.01430554128   0.48588588       0.0000       0.0000 0.0020
## [578,]  -0.08815333060   2.40372903       0.0000       0.0000 0.0028
## [579,]   0.00582497679   0.29124884       0.0000       0.0000 0.0004
## [580,]  -0.01142494628   0.52346414       0.0000       0.0000 0.0016
## [581,]   0.02753175821   1.40647616       0.0000       0.0000 0.0024
## [582,]  -0.01894588797   0.48190002       0.0000       0.0000 0.0024
## [583,]  -0.02627250839   0.71948713       0.0000       0.0000 0.0036
## [584,]   0.00648849596   0.38079587       0.0000       0.0000 0.0028
## [585,]   0.00731855564   0.28155153       0.0000       0.0000 0.0012
## [586,]   0.01983864947   1.60780459       0.0000       0.0000 0.0024
## [587,]   0.02602032400   1.98907284       0.0000       0.0000 0.0032
## [588,]  -0.00971600188   0.48142734       0.0000       0.0000 0.0016
## [589,]  -0.01130402076   0.56132594       0.0000       0.0000 0.0016
## [590,]  -0.00183928680   0.08271597       0.0000       0.0000 0.0012
## [591,]  -0.01008355679   0.62035910       0.0000       0.0000 0.0028
## [592,]   0.05165779553   1.47319837       0.0000       0.0000 0.0032
## [593,]  -0.01076681449   0.34278875       0.0000       0.0000 0.0016
## [594,]  -0.02740375119   0.98266534       0.0000       0.0000 0.0016
## [595,]   0.02013928278   0.76163198       0.0000       0.0000 0.0024
## [596,]  -0.03508871586   1.10603745       0.0000       0.0000 0.0028
## [597,]  -0.00954551638   0.73788880       0.0000       0.0000 0.0032
## [598,]  -0.09446078137   3.34773177       0.0000       0.0000 0.0040
## [599,]   0.10834766223   2.70082842       0.0000       0.0000 0.0024
## [600,]  -0.09240618984   2.59372970       0.0000       0.0000 0.0032
## [601,]  -0.02190125349   0.77537479       0.0000       0.0000 0.0028
## [602,]  -0.02868634973   0.59973893       0.0000       0.0000 0.0032
## [603,]  -0.01819313300   0.89867401       0.0000       0.0000 0.0012
## [604,]  -0.00537841399   0.39688330       0.0000       0.0000 0.0020
## [605,]  -0.00339343771   0.17707602       0.0000       0.0000 0.0012
## [606,]  -0.01586103350   0.55646592       0.0000       0.0000 0.0012
## [607,]  -0.00607217846   0.50909934       0.0000       0.0000 0.0036
## [608,]  -0.03658321050   0.74803917       0.0000       0.0000 0.0032
## [609,]  -0.02350853148   0.74293023       0.0000       0.0000 0.0016
## [610,]  -0.04912853882   2.23633880       0.0000       0.0000 0.0032
## [611,]  -0.00445920780   0.35385549       0.0000       0.0000 0.0016
## [612,]   0.02125139759   0.75268509       0.0000       0.0000 0.0024
## [613,]  -0.02172493053   0.66243557       0.0000       0.0000 0.0028
## [614,]   0.00199485064   0.24116347       0.0000       0.0000 0.0016
## [615,]  -0.01119982498   0.47508304       0.0000       0.0000 0.0032
## [616,]  -0.15748938011   3.96079275       0.0000       0.0000 0.0028
## [617,]  -0.04545088637   1.33131779       0.0000       0.0000 0.0020
## [618,]  -0.03282793641   1.01009899       0.0000       0.0000 0.0032
## [619,]   0.01747802931   1.23625706       0.0000       0.0000 0.0032
## [620,]  -0.05312224191   1.91660079       0.0000       0.0000 0.0020
## [621,]   0.00000000000   0.00000000       0.0000       0.0000 0.0000
## [622,]  -0.19286966594   3.76289013       0.0000       0.0000 0.0064
## [623,]  -0.05443974094   2.06035293       0.0000       0.0000 0.0020
## [624,]  -0.04038764877   0.99933868       0.0000       0.0000 0.0032
## [625,]   0.00411212282   0.33655114       0.0000       0.0000 0.0032
## [626,]   0.00262265315   0.13113266       0.0000       0.0000 0.0004
## [627,]  -0.01693170606   0.45041393       0.0000       0.0000 0.0036
## [628,]  -0.00809910132   0.42957659       0.0000       0.0000 0.0016
## [629,]  -0.04589090208   0.98951040       0.0000       0.0000 0.0036
## [630,]  -0.00121992104   0.25501943       0.0000       0.0000 0.0016
## [631,]   0.00036591234   0.01829562       0.0000       0.0000 0.0004
## [632,]  -0.17257243953   3.08728681       0.0000       0.0000 0.0080
## [633,]  -0.01107524767   0.46911352       0.0000       0.0000 0.0020
## [634,]  -0.02017955861   1.02304984       0.0000       0.0000 0.0012
## [635,]  -0.01295070475   0.57375942       0.0000       0.0000 0.0020
## [636,]  -0.00713746392   0.56751840       0.0000       0.0000 0.0024
## [637,]  -0.03376105122   1.17020773       0.0000       0.0000 0.0024
## [638,]  -0.00989327328   0.33591242       0.0000       0.0000 0.0020
## [639,]  -0.00256533956   0.36739966       0.0000       0.0000 0.0016
## [640,]  -0.00269028292   0.37933905       0.0000       0.0000 0.0012
## [641,]  -0.00963783906   1.03972071       0.0000       0.0000 0.0024
## [642,]  -0.02124043579   1.04050109       0.0000       0.0000 0.0016
## [643,]  -0.00013314138   0.33137009       0.0000       0.0000 0.0020
## [644,]   0.00115447198   0.52930014       0.0000       0.0000 0.0016
## [645,]   0.01349330416   0.79277828       0.0000       0.0000 0.0028
## [646,]  -0.13146962722   2.90184766       0.0000       0.0000 0.0040
## [647,]  -0.00844679896   0.69038141       0.0000       0.0000 0.0020
## [648,]   0.00148019569   0.33650714       0.0000       0.0000 0.0024
## [649,]   0.00107936657   0.49317648       0.0000       0.0000 0.0028
## [650,]  -0.04838680123   1.09978452       0.0000       0.0000 0.0028
## [651,]   0.00002731102   0.34128801       0.0000       0.0000 0.0016
## [652,]  -0.00983561295   0.33562587       0.0000       0.0000 0.0012
## [653,]   0.01361635077   0.40605488       0.0000       0.0000 0.0012
## [654,]  -0.00192308137   0.16579172       0.0000       0.0000 0.0008
## [655,]  -0.02944831288   1.41661508       0.0000       0.0000 0.0008
## [656,]  -0.01037220382   0.31893413       0.0000       0.0000 0.0024
## [657,]  -0.00925471576   0.60974452       0.0000       0.0000 0.0036
## [658,]   0.00527591694   0.26379585       0.0000       0.0000 0.0004
## [659,]  -0.00335552470   0.52713649       0.0000       0.0000 0.0024
## [660,]  -0.01209702695   0.59328194       0.0000       0.0000 0.0020
## [661,]  -0.01733385276   0.84580107       0.0000       0.0000 0.0036
## [662,]  -0.00896371809   0.55639967       0.0000       0.0000 0.0024
## [663,]   0.00924620893   0.34937777       0.0000       0.0000 0.0024
## [664,]  -0.00087552466   0.36674731       0.0000       0.0000 0.0012
## [665,]  -0.01040482765   0.99927262       0.0000       0.0000 0.0024
## [666,]   0.00480427342   0.21088040       0.0000       0.0000 0.0008
## [667,]   0.00298379021   0.13215909       0.0000       0.0000 0.0008
## [668,]   0.00354924993   0.19650710       0.0000       0.0000 0.0020
## [669,]  -0.10424088377   3.77536817       0.0000       0.0000 0.0032
## [670,]  -0.00727880764   0.80374376       0.0000       0.0000 0.0028
## [671,]   0.00621117048   0.31055852       0.0000       0.0000 0.0004
## [672,]   0.00842008502   0.35715397       0.0000       0.0000 0.0016
## [673,]  -0.00265938357   0.20680760       0.0000       0.0000 0.0008
## [674,]  -0.00501152234   0.69124209       0.0000       0.0000 0.0036
## [675,]  -0.00355356612   0.37285235       0.0000       0.0000 0.0016
## [676,]  -0.00513795454   0.45422770       0.0000       0.0000 0.0028
## [677,]   0.38405494940   5.57276673       0.0000       0.0000 0.0072
## [678,]  -0.01395056082   0.67612886       0.0000       0.0000 0.0020
## [679,]  -0.00669660542   0.49493155       0.0000       0.0000 0.0016
## [680,]  -0.01556330413   0.47298986       0.0000       0.0000 0.0016
## [681,]   0.00629475283   0.29087253       0.0000       0.0000 0.0008
## [682,]  -0.00088703025   0.04435151       0.0000       0.0000 0.0004
## [683,]  -0.01796041531   0.89802077       0.0000       0.0000 0.0004
## [684,]  -0.04612964407   0.90773034       0.0000       0.0000 0.0040
## [685,]  -0.01850991613   0.47486439       0.0000       0.0000 0.0032
## [686,]  -0.03578881374   1.03637612       0.0000       0.0000 0.0024
## [687,]  -0.00102821255   0.17560270       0.0000       0.0000 0.0016
## [688,]  -0.03315282258   0.81850228       0.0000       0.0000 0.0020
## [689,]   0.00363826223   0.18625282       0.0000       0.0000 0.0016
## [690,]  -0.01099718786   1.51015482       0.0000       0.0000 0.0024
## [691,]  -0.01716996373   0.82623306       0.0000       0.0000 0.0032
## [692,]   0.03075069310   1.98626552       0.0000       0.0000 0.0016
## [693,]  -0.00786662130   0.28496282       0.0000       0.0000 0.0008
## [694,]  -0.01686672059   0.75953854       0.0000       0.0000 0.0028
## [695,]   0.02823695619   2.08139949       0.0000       0.0000 0.0032
## [696,]   0.03124882673   1.93904513       0.0000       0.0000 0.0024
## [697,]  -0.00846355312   0.60931349       0.0000       0.0000 0.0024
## [698,]  -0.04285784756   1.60880208       0.0000       0.0000 0.0016
## [699,]   0.01736235986   0.62512042       0.0000       0.0000 0.0016
## [700,]  -0.09184617746   2.30101104       0.0000       0.0000 0.0044
## [701,]  -0.01214252302   0.73769567       0.0000       0.0000 0.0020
## [702,]  -0.37227601981   5.56141530       0.0000       0.0000 0.0080
## [703,]   1.05503591250  11.61964145       0.0000       0.0000 0.0112
## [704,]  -0.00355271823   0.26910166       0.0000       0.0000 0.0012
## [705,]  -0.00537482556   0.33114357       0.0000       0.0000 0.0016
## [706,]  -0.05631042818   2.46432860       0.0000       0.0000 0.0012
## [707,]  -0.00188057696   0.51914149       0.0000       0.0000 0.0020
## [708,]  -0.01662849038   0.51727536       0.0000       0.0000 0.0028
## [709,]  -0.00337402209   0.23792173       0.0000       0.0000 0.0012
## [710,]  -0.01444002128   0.35382363       0.0000       0.0000 0.0020

4.2.4 Predict fitted values for each individual

pred.npb <- predict(fit.npb)
fittedvals <- pred.npb$fitted.vals

4.2.5 Plot predicted outcomes against “measured” outcomes

plot(fittedvals, Y)
abline(a = 0, b = 1, col = "red")

4.3 Fit the NPB model without ozone

Only ozone shows up in the NPB model. However, there is some speculation that ozone is just a proxy for some of the other variables. Here I am running the NPB model without ozone just to see if something else pops up instead.

priors.npb <- priors.npb.24

#' Exposures
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "pct_tree_cover"     
##  [4] "pct_impervious"      "mean_aadt_intensity" "dist_m_tri"         
##  [7] "dist_m_npl"          "dist_m_waste_site"   "dist_m_major_emit"  
## [10] "dist_m_cafo"         "dist_m_mine_well"    "cvd_rate_adj"       
## [13] "res_rate_adj"        "violent_crime_rate"  "property_crime_rate"
## [16] "pct_less_hs"         "pct_unemp"           "pct_limited_eng"    
## [19] "pct_hh_pov"          "pct_poc"
X.scaled2 <- X.scaled[,-c(2)]
colnames(X.scaled2)
##  [1] "mean_pm"             "pct_tree_cover"      "pct_impervious"     
##  [4] "mean_aadt_intensity" "dist_m_tri"          "dist_m_npl"         
##  [7] "dist_m_waste_site"   "dist_m_major_emit"   "dist_m_cafo"        
## [10] "dist_m_mine_well"    "cvd_rate_adj"        "res_rate_adj"       
## [13] "violent_crime_rate"  "property_crime_rate" "pct_less_hs"        
## [16] "pct_unemp"           "pct_limited_eng"     "pct_hh_pov"         
## [19] "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
# fit.npb2 <- npb(niter = 5000, nburn = 2500, X = X.scaled2, Y = Y, W = W.scaled2,
#                 scaleY = TRUE,
#                 priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb2, file = here::here("Results", "NPB_Birth_Weight_v3.2.rdata"))

load(here::here("Results", "NPB_Birth_Weight_v3.2.rdata"))
npb.sum2 <- summary(fit.npb2)

4.3.1 First, main effect regression coefficients with PIPs

rownames(npb.sum2$main.effects) <- colnames(X.scaled2)
npb.sum2$main.effects
##                     Posterior Mean        SD 95% CI Lower 95% CI Upper    PIP
## mean_pm                  0.4407640  6.481440   -12.161629    18.073865 0.2564
## pct_tree_cover           0.2642844  5.907754   -12.367591    15.955959 0.2508
## pct_impervious          -0.9324881  6.452437   -17.545274     9.331679 0.2380
## mean_aadt_intensity      0.4357418  5.601033   -10.521010    15.787301 0.2464
## dist_m_tri               0.1581616  6.262555   -13.957391    16.556472 0.2772
## dist_m_npl               1.1673370  6.973845    -9.358043    22.024409 0.2660
## dist_m_waste_site        4.8288396 12.792222    -6.853881    45.524547 0.3356
## dist_m_major_emit        1.3269033  7.462049    -9.148800    25.099342 0.2588
## dist_m_cafo             -1.9694753 18.626634   -42.182813    24.084298 0.3276
## dist_m_mine_well        -2.0373787  9.241124   -29.332014    10.564666 0.2944
## cvd_rate_adj            -1.1051803  6.716039   -19.079850     9.810397 0.2676
## res_rate_adj            -1.6056014  7.214406   -23.176058     8.434401 0.2684
## violent_crime_rate       0.2620968  5.943370   -10.631896    15.787301 0.2528
## property_crime_rate     -1.0638364  5.922815   -18.092789     8.630678 0.2536
## pct_less_hs             -0.5034778  7.128440   -16.487666    14.445030 0.2748
## pct_unemp               -9.3706142 19.159359   -67.673376     3.109754 0.4120
## pct_limited_eng         -0.6049911  6.549114   -15.795377    11.534563 0.2500
## pct_hh_pov              -0.3708097  6.801363   -15.364005    12.755524 0.2524
## pct_poc                  0.3869594  7.286020   -13.829870    19.624174 0.2720
#' Which one's have PIPs > 0.5
# selected_exp2 <- which(npb.sum2$main.effects[,"PIP"] >= 0.5)
# selected_exp2

4.3.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum2$interactions
##        Posterior Mean         SD 95% CI Lower 95% CI Upper    PIP
##   [1,]  0.00070489986  0.2615722            0            0 0.0040
##   [2,] -0.00228693613  0.3715087            0            0 0.0072
##   [3,]  0.00647121899  0.5343933            0            0 0.0060
##   [4,]  0.00044081434  0.3101090            0            0 0.0060
##   [5,] -0.00745209726  0.4937818            0            0 0.0064
##   [6,] -0.01560976678  0.4720498            0            0 0.0052
##   [7,] -0.01722247659  0.5852312            0            0 0.0068
##   [8,] -0.04930647285  1.1052879            0            0 0.0084
##   [9,] -0.02526369977  0.8438638            0            0 0.0068
##  [10,] -0.01003786971  0.3301583            0            0 0.0052
##  [11,]  0.00095854730  0.9508631            0            0 0.0076
##  [12,] -0.03813887461  0.9465690            0            0 0.0068
##  [13,] -0.03244939866  0.7384257            0            0 0.0056
##  [14,] -0.02060545794  0.5279291            0            0 0.0052
##  [15,] -0.00884382385  0.3674973            0            0 0.0036
##  [16,] -0.04760286638  1.0706389            0            0 0.0076
##  [17,]  0.00390734679  0.3389511            0            0 0.0040
##  [18,]  0.00283095104  0.5579978            0            0 0.0068
##  [19,]  0.00036777783  0.6876817            0            0 0.0060
##  [20,]  0.00534721851  0.4136275            0            0 0.0060
##  [21,]  0.01819477404  0.5408361            0            0 0.0056
##  [22,]  0.00153988848  0.4458849            0            0 0.0048
##  [23,]  0.00983877229  0.7662673            0            0 0.0056
##  [24,]  0.01327967636  0.5057805            0            0 0.0072
##  [25,] -0.01184554525  0.4089115            0            0 0.0064
##  [26,] -0.03954456420  0.8499696            0            0 0.0060
##  [27,] -0.03552106601  1.0235001            0            0 0.0060
##  [28,] -0.00306169494  0.7856794            0            0 0.0052
##  [29,] -0.02848579398  0.6073078            0            0 0.0056
##  [30,]  0.00553802648  0.3980201            0            0 0.0060
##  [31,] -0.05544807950  1.2544435            0            0 0.0052
##  [32,]  0.00289600399  0.2860713            0            0 0.0052
##  [33,]  0.00096869062  0.5623342            0            0 0.0068
##  [34,] -0.00627907970  0.2522949            0            0 0.0040
##  [35,] -0.00857757876  0.2359099            0            0 0.0044
##  [36,]  0.02350558424  1.1531182            0            0 0.0060
##  [37,]  0.03492129619  0.8794809            0            0 0.0080
##  [38,]  0.00084278122  0.3552540            0            0 0.0044
##  [39,]  0.00765313480  0.4884620            0            0 0.0048
##  [40,]  0.01626896815  0.4310151            0            0 0.0056
##  [41,]  0.00795417135  0.3789797            0            0 0.0036
##  [42,] -0.00999666034  0.5214566            0            0 0.0048
##  [43,] -0.01850419331  0.6488152            0            0 0.0040
##  [44,] -0.01442520183  0.4369560            0            0 0.0052
##  [45,] -0.02109882891  0.5472945            0            0 0.0052
##  [46,] -0.00601939666  0.5804819            0            0 0.0056
##  [47,] -0.00395211894  0.4725794            0            0 0.0036
##  [48,] -0.03881909268  0.8444165            0            0 0.0048
##  [49,]  0.01195977696  0.5582980            0            0 0.0076
##  [50,] -0.01182785804  0.4862868            0            0 0.0068
##  [51,] -0.00873685811  0.2045007            0            0 0.0024
##  [52,] -0.00371656961  0.5593697            0            0 0.0064
##  [53,]  0.01236884699  0.3599505            0            0 0.0032
##  [54,] -0.00309728546  0.2999571            0            0 0.0032
##  [55,]  0.04599311665  1.2600665            0            0 0.0052
##  [56,] -0.02954062525  0.6218568            0            0 0.0060
##  [57,] -0.04559485714  1.0986161            0            0 0.0080
##  [58,] -0.06723551558  1.0571497            0            0 0.0092
##  [59,] -0.03619309295  0.8931806            0            0 0.0052
##  [60,] -0.05971955536  1.0841527            0            0 0.0096
##  [61,] -0.03960603157  0.6793694            0            0 0.0064
##  [62,]  0.02075926153  0.8585117            0            0 0.0048
##  [63,] -0.00557993815  0.5279123            0            0 0.0056
##  [64,]  0.01707334964  0.6388643            0            0 0.0092
##  [65,]  0.01293984973  0.5391502            0            0 0.0060
##  [66,]  0.04169749849  1.1045298            0            0 0.0080
##  [67,] -0.00752068963  0.3619287            0            0 0.0060
##  [68,] -0.01481281705  0.3604213            0            0 0.0064
##  [69,]  0.01830690909  0.3966702            0            0 0.0052
##  [70,] -0.00752346119  0.3411635            0            0 0.0068
##  [71,] -0.02449631332  0.8634536            0            0 0.0080
##  [72,]  0.02037321089  0.5818778            0            0 0.0048
##  [73,]  0.00502085279  0.3602976            0            0 0.0044
##  [74,] -0.00249885312  0.5100230            0            0 0.0076
##  [75,]  0.01009107123  0.5002083            0            0 0.0036
##  [76,] -0.00422637989  0.5636386            0            0 0.0076
##  [77,]  0.01431627035  0.6027884            0            0 0.0072
##  [78,]  0.04900323863  1.7263292            0            0 0.0068
##  [79,] -0.00926932812  0.7337227            0            0 0.0052
##  [80,]  0.00037742863  0.2155910            0            0 0.0036
##  [81,] -0.00261599525  0.3441624            0            0 0.0036
##  [82,] -0.00459069147  0.4074966            0            0 0.0052
##  [83,] -0.00312319212  0.3472492            0            0 0.0064
##  [84,] -0.00502038697  0.5803227            0            0 0.0072
##  [85,] -0.00092574006  0.4456749            0            0 0.0048
##  [86,]  0.00071849739  0.7735737            0            0 0.0056
##  [87,] -0.00564820929  0.3948624            0            0 0.0056
##  [88,] -0.01186822075  0.3374591            0            0 0.0076
##  [89,] -0.01747643069  0.8364548            0            0 0.0080
##  [90,] -0.00031630302  0.2228517            0            0 0.0032
##  [91,] -0.00513956643  0.5465570            0            0 0.0044
##  [92,] -0.02032438390  0.5379958            0            0 0.0060
##  [93,] -0.01771887427  0.4873413            0            0 0.0072
##  [94,]  0.04650096556  1.3776472            0            0 0.0064
##  [95,]  0.01236704805  0.4577457            0            0 0.0060
##  [96,] -0.00331224680  0.5194041            0            0 0.0088
##  [97,] -0.01499898251  0.6970688            0            0 0.0044
##  [98,]  0.00281379055  0.5895343            0            0 0.0064
##  [99,]  0.00139653498  0.5079189            0            0 0.0052
## [100,]  0.00120670233  0.9336013            0            0 0.0084
## [101,] -0.02641595216  0.5640905            0            0 0.0072
## [102,]  0.00398614422  0.7135476            0            0 0.0084
## [103,]  0.01793837783  0.7336196            0            0 0.0056
## [104,]  0.01650775948  0.9337035            0            0 0.0060
## [105,] -0.00655069219  0.4279052            0            0 0.0036
## [106,]  0.06058987851  1.1328023            0            0 0.0068
## [107,]  0.09911197562  2.0512419            0            0 0.0096
## [108,] -0.02891819707  0.8225235            0            0 0.0068
## [109,] -0.00231398495  0.4151320            0            0 0.0052
## [110,]  0.00154357333  0.7002825            0            0 0.0056
## [111,] -0.02620142600  0.8172581            0            0 0.0068
## [112,] -0.05705722631  1.1805650            0            0 0.0080
## [113,] -0.06392313596  1.0213473            0            0 0.0076
## [114,] -0.03846456579  0.7170430            0            0 0.0060
## [115,] -0.02171772408  0.6109252            0            0 0.0048
## [116,] -0.03653445798  0.8464495            0            0 0.0084
## [117,] -0.13397927382  1.7740826            0            0 0.0108
## [118,] -0.01138691331  0.4832909            0            0 0.0056
## [119,] -0.00884811397  0.4199687            0            0 0.0048
## [120,]  0.00632859515  0.9014699            0            0 0.0068
## [121,] -0.05077466301  1.0327486            0            0 0.0080
## [122,]  0.00765786788  0.6810144            0            0 0.0064
## [123,] -0.00196373832  0.2702260            0            0 0.0036
## [124,] -0.00125093108  0.1620005            0            0 0.0024
## [125,] -0.02800549721  0.8822045            0            0 0.0076
## [126,]  0.00155738570  0.3025590            0            0 0.0036
## [127,]  0.03541058261  0.9397232            0            0 0.0064
## [128,]  0.00495947166  0.4609332            0            0 0.0068
## [129,] -0.00326818867  0.3692611            0            0 0.0052
## [130,] -0.00233304989  0.2136014            0            0 0.0052
## [131,]  0.05317464528  1.3974681            0            0 0.0080
## [132,]  0.01406169965  0.6594691            0            0 0.0052
## [133,]  0.49001917089  5.8146484            0            0 0.0136
## [134,]  0.05485676610  1.0593256            0            0 0.0080
## [135,]  0.00711457178  0.4471329            0            0 0.0052
## [136,] -0.03538955853  0.6191723            0            0 0.0080
## [137,] -0.02560688919  0.6896599            0            0 0.0076
## [138,] -0.00752127037  0.5527645            0            0 0.0060
## [139,] -0.04619677140  0.9190235            0            0 0.0060
## [140,] -0.14507279021  2.0219541            0            0 0.0116
## [141,] -0.08073266278  1.4204093            0            0 0.0060
## [142,] -0.05478732497  1.1591969            0            0 0.0084
## [143,] -0.01411157365  0.4709223            0            0 0.0060
## [144,]  0.00124096398  0.5080511            0            0 0.0040
## [145,] -0.03650705038  0.5567967            0            0 0.0084
## [146,] -0.00054504292  0.2647096            0            0 0.0048
## [147,] -0.01901002844  0.5990556            0            0 0.0052
## [148,] -0.02208171703  0.7925612            0            0 0.0056
## [149,] -0.06025033956  1.1721792            0            0 0.0112
## [150,] -0.01797097373  0.5179402            0            0 0.0048
## [151,] -0.00043596601  0.1932877            0            0 0.0020
## [152,] -0.00132771634  0.4159105            0            0 0.0060
## [153,]  0.01580619997  0.5363260            0            0 0.0048
## [154,] -0.01812550481  0.8799809            0            0 0.0072
## [155,] -0.00728206481  0.5532069            0            0 0.0052
## [156,] -0.01750032061  0.5131339            0            0 0.0092
## [157,] -0.00215401420  0.3863265            0            0 0.0060
## [158,] -0.00547020581  0.3774329            0            0 0.0044
## [159,] -0.01732653512  0.5032522            0            0 0.0076
## [160,] -0.00829996462  0.3867090            0            0 0.0048
## [161,]  0.00073871334  0.3396756            0            0 0.0040
## [162,] -0.01974418026  0.4289083            0            0 0.0036
## [163,] -0.00757527808  0.4033045            0            0 0.0064
## [164,]  0.00661386272  0.5005326            0            0 0.0044
## [165,]  0.00663509290  0.4258373            0            0 0.0056
## [166,] -0.04015636860  0.6822646            0            0 0.0092
## [167,] -0.01213560497  0.2349939            0            0 0.0040
## [168,] -0.03690853239  0.8054190            0            0 0.0064
## [169,] -0.01085518400  0.2717385            0            0 0.0024
## [170,] -0.01745282921  0.5355195            0            0 0.0072
## [171,] -0.00238737171  0.2665765            0            0 0.0056
## [172,]  0.02632751133  0.6937801            0            0 0.0068
## [173,] -0.00567219658  0.1775832            0            0 0.0024
## [174,] -0.02584536998  0.9371089            0            0 0.0072
## [175,] -0.01243660795  0.6214533            0            0 0.0076
## [176,] -0.01776225129  0.6173365            0            0 0.0060
## [177,] -0.02735033051  1.7185967            0            0 0.0056
## [178,]  0.00296093452  0.5550833            0            0 0.0040
## [179,] -0.01790246252  0.5489640            0            0 0.0060
## [180,] -0.05639952785  1.9715923            0            0 0.0060
## [181,]  0.05978874560  2.8004915            0            0 0.0076
## [182,] -0.00409735919  0.4056986            0            0 0.0048
## [183,] -0.11620891453  2.3429277            0            0 0.0084
## [184,]  0.00142217386  1.2541414            0            0 0.0052
## [185,]  0.03791978638  2.4993117            0            0 0.0040
## [186,] -0.02427666623  1.1758766            0            0 0.0096
## [187,] -0.00382374810  0.5586660            0            0 0.0080
## [188,]  0.00804213071  0.8606906            0            0 0.0052
## [189,] -0.01614257921  0.4404526            0            0 0.0044
## [190,]  0.03011143628  1.8892571            0            0 0.0088
## [191,] -0.02632728070  2.6802782            0            0 0.0076
## [192,] -0.01247531692  0.6831917            0            0 0.0064
## [193,] -0.01992782855  0.7551196            0            0 0.0064
## [194,] -0.02569575952  0.8409469            0            0 0.0072
## [195,]  0.02070331241  0.6620814            0            0 0.0056
## [196,] -0.00099765402  0.5864973            0            0 0.0056
## [197,] -0.01826118635  1.2958518            0            0 0.0080
## [198,]  0.00201362987  0.5702392            0            0 0.0060
## [199,]  0.00907817216  0.5525795            0            0 0.0040
## [200,]  0.00663113292  0.6013125            0            0 0.0072
## [201,]  0.01780886452  0.9931680            0            0 0.0080
## [202,] -0.01022174485  1.2676993            0            0 0.0036
## [203,]  0.00584374813  0.9086611            0            0 0.0108
## [204,]  0.09194412836  4.0122338            0            0 0.0048
## [205,] -0.07357915436  1.6723127            0            0 0.0068
## [206,]  0.00624726554  1.1210794            0            0 0.0084
## [207,] -0.05333540884  1.1251248            0            0 0.0044
## [208,] -0.04375621433  1.9794587            0            0 0.0080
## [209,] -0.01351125037  0.5946946            0            0 0.0060
## [210,]  0.05863792300  2.6404118            0            0 0.0096
## [211,] -0.00096086308  1.0645666            0            0 0.0060
## [212,]  0.00574496273  1.3132124            0            0 0.0076
## [213,]  0.01790392832  0.7959548            0            0 0.0044
## [214,]  0.00504234547  0.7193679            0            0 0.0056
## [215,]  0.01354150577  0.9879442            0            0 0.0064
## [216,] -0.07383875569  1.8667502            0            0 0.0080
## [217,] -0.01953994489  0.8973242            0            0 0.0076
## [218,] -0.00710454278  0.7895527            0            0 0.0068
## [219,]  0.10007541265  3.1316669            0            0 0.0080
## [220,]  0.01829153935  0.4038324            0            0 0.0052
## [221,]  0.00338157467  0.2940353            0            0 0.0056
## [222,] -0.01754029575  0.7890203            0            0 0.0052
## [223,] -0.02032804718  0.8156395            0            0 0.0044
## [224,] -0.00665285473  0.3569734            0            0 0.0052
## [225,] -0.04001144521  0.7536756            0            0 0.0080
## [226,] -0.01182119632  0.3686393            0            0 0.0048
## [227,] -0.01513177805  0.5248259            0            0 0.0060
## [228,]  0.03125165085  1.0896912            0            0 0.0076
## [229,] -0.01077345619  0.4618529            0            0 0.0060
## [230,]  0.01120016478  2.2415704            0            0 0.0092
## [231,] -0.00300239355  0.9610564            0            0 0.0060
## [232,] -0.01771344116  0.8742269            0            0 0.0088
## [233,] -0.03557925470  1.5956718            0            0 0.0072
## [234,] -0.02790083765  1.2610581            0            0 0.0108
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## [519,] -0.05987911429  1.4553599            0            0 0.0068
## [520,] -0.11906474785  4.2424177            0            0 0.0080
## [521,] -0.14453943388  2.8835544            0            0 0.0108
## [522,]  0.02173356275  0.7212922            0            0 0.0056
## [523,]  0.01129156554  0.5012139            0            0 0.0036
## [524,] -0.01042194281  0.5293519            0            0 0.0084
## [525,] -0.01536968497  0.7271904            0            0 0.0056
## [526,] -0.04404686419  1.9728043            0            0 0.0068
## [527,] -0.00632791765  0.9339384            0            0 0.0092
## [528,] -0.03705217161  0.8099271            0            0 0.0048
## [529,] -0.01348837922  0.6945416            0            0 0.0060
## [530,]  0.03256597547  0.8233571            0            0 0.0060
## [531,]  0.00433042817  0.8778111            0            0 0.0080
## [532,] -0.02684805637  0.9463427            0            0 0.0056
## [533,] -0.08246887237  1.5292165            0            0 0.0088
## [534,] -0.01886106065  0.7569910            0            0 0.0060
## [535,] -0.05144934758  1.2555387            0            0 0.0080
## [536,] -0.00099964129  0.5883518            0            0 0.0052
## [537,] -0.06475441667  1.4126420            0            0 0.0068
## [538,] -0.02251677833  0.8307205            0            0 0.0072
## [539,] -0.01358603036  0.5788411            0            0 0.0060
## [540,]  0.01900190000  1.1585567            0            0 0.0076
## [541,] -0.02279796865  0.7112741            0            0 0.0044
## [542,] -0.02334423527  0.8232008            0            0 0.0068
## [543,]  0.03083240425  0.9701480            0            0 0.0060
## [544,] -0.03739440537  1.3359142            0            0 0.0092
## [545,] -0.06186586131  1.3161702            0            0 0.0080
## [546,] -0.00788504592  1.4848881            0            0 0.0072
## [547,]  0.10037175021  2.6271471            0            0 0.0088
## [548,]  0.01033344274  0.5416129            0            0 0.0048
## [549,] -0.09288551530  2.9735232            0            0 0.0076
## [550,]  0.00072463394  0.6618185            0            0 0.0044
## [551,] -0.10218023774  2.2758304            0            0 0.0072
## [552,] -0.00968645740  0.7425965            0            0 0.0064
## [553,] -0.09180750490  1.9950580            0            0 0.0092
## [554,]  0.14817095904  3.2651406            0            0 0.0072
## [555,] -0.10806249737  2.2329092            0            0 0.0088
## [556,]  0.00392828102  0.5700473            0            0 0.0092
## [557,] -0.01980664286  0.5053938            0            0 0.0060
## [558,]  0.05307375585  1.5622932            0            0 0.0068
## [559,] -0.02246959669  0.7922375            0            0 0.0080
## [560,]  0.00805816887  0.4324853            0            0 0.0064
## [561,] -0.03274436257  0.9539404            0            0 0.0072
## [562,]  0.00393151581  0.7113762            0            0 0.0044
## [563,] -0.03638787429  0.8537371            0            0 0.0084
## [564,] -0.06701297344  1.1124659            0            0 0.0080
## [565,] -0.07725131918  2.2615023            0            0 0.0096
## [566,] -0.00928118976  0.7858176            0            0 0.0060
## [567,] -0.03335090435  0.7809843            0            0 0.0040
## [568,] -0.14840499101  3.9228124            0            0 0.0092
## [569,] -0.01861345176  0.5506965            0            0 0.0088
## [570,] -0.02361738580  0.7139254            0            0 0.0072
## [571,] -0.14502999830  2.9696430            0            0 0.0072
## [572,] -0.03580922781  1.1655563            0            0 0.0060
## [573,] -0.05951573900  1.3704253            0            0 0.0064
## [574,] -0.01424506487  0.8366104            0            0 0.0068
## [575,] -0.04016379260  1.6506645            0            0 0.0072
## [576,] -0.02413716008  0.6051806            0            0 0.0052
## [577,] -0.15027500818  2.8389735            0            0 0.0076
## [578,] -0.05556391348  1.2316867            0            0 0.0080
## [579,] -0.09997429333  1.7019048            0            0 0.0100
## [580,]  0.00360443450  0.9967971            0            0 0.0048
## [581,] -0.02038420876  0.7872548            0            0 0.0044
## [582,] -0.01322948473  0.5084871            0            0 0.0068
## [583,] -0.02400532523  0.7729448            0            0 0.0064
## [584,] -0.09079851712  1.9482808            0            0 0.0076
## [585,] -0.00869038460  0.4732573            0            0 0.0056
## [586,]  0.01287399401  0.4050116            0            0 0.0064
## [587,] -0.28517640587  4.0119864            0            0 0.0128
## [588,] -0.02657993511  1.0656853            0            0 0.0052
## [589,] -0.15732143483  2.5128629            0            0 0.0092
## [590,] -0.02050218167  0.9533988            0            0 0.0064
## [591,] -0.02448282558  0.5783263            0            0 0.0036
## [592,]  0.03067515932  1.2363184            0            0 0.0064
## [593,]  0.01012489384  0.7951166            0            0 0.0068
## [594,] -0.00296578181  0.6174908            0            0 0.0060
## [595,]  0.01958418880  1.4058722            0            0 0.0048
## [596,] -0.02245148855  0.7288340            0            0 0.0060
## [597,] -0.00297965647  0.6886126            0            0 0.0048
## [598,]  0.00826010160  1.5868813            0            0 0.0084
## [599,] -0.00903424632  1.1399129            0            0 0.0072
## [600,]  0.03235800371  1.1119928            0            0 0.0052
## [601,] -0.10242322752  2.2465206            0            0 0.0084
## [602,] -0.02320464626  1.6876933            0            0 0.0076
## [603,] -0.02184780020  0.5963628            0            0 0.0036
## [604,] -0.00151015342  1.5445703            0            0 0.0072
## [605,] -0.13688680542  2.2526437            0            0 0.0120
## [606,]  0.12233961389  3.0290075            0            0 0.0096
## [607,] -0.17022078113  3.2556028            0            0 0.0112
## [608,] -0.01424318968  0.3431607            0            0 0.0048
## [609,] -0.02756855277  1.3592225            0            0 0.0064
## [610,] -0.01835903005  0.8810822            0            0 0.0084
## [611,] -0.02116144171  0.6228565            0            0 0.0052
## [612,] -0.00861212027  0.3816419            0            0 0.0044
## [613,] -0.03644205680  1.2435053            0            0 0.0080
## [614,] -0.00029113491  0.9778448            0            0 0.0072
## [615,] -0.05095436566  1.1801820            0            0 0.0100
## [616,] -0.03644181179  1.0931629            0            0 0.0072
## [617,]  0.01225762336  0.9418062            0            0 0.0080
## [618,] -0.00588046246  0.6369702            0            0 0.0056
## [619,]  0.00732379180  1.6487593            0            0 0.0080
## [620,] -0.01365837600  0.6997623            0            0 0.0068
## [621,] -0.03490604650  1.0929314            0            0 0.0076
## [622,] -0.05382299268  1.3324162            0            0 0.0100
## [623,] -0.02937780475  0.6511281            0            0 0.0056
## [624,] -0.19678922634  5.0153489            0            0 0.0064
## [625,] -0.06102762318  1.4082121            0            0 0.0060
## [626,] -0.01799875044  0.8192186            0            0 0.0092
## [627,] -0.01922824811  0.8426396            0            0 0.0080
## [628,] -0.01942748523  0.4414635            0            0 0.0048
## [629,] -0.10212021527  2.4015833            0            0 0.0076
## [630,] -0.03255109354  1.2734485            0            0 0.0064
## [631,] -0.02162793219  0.6299233            0            0 0.0064
## [632,]  0.38514942054  4.5237266            0            0 0.0152
## [633,] -0.12891188299  2.4083169            0            0 0.0092
## [634,] -0.00553075917  0.6266780            0            0 0.0052
## [635,] -0.05236693722  1.1113923            0            0 0.0056
## [636,]  0.01208057029  0.4053658            0            0 0.0056
## [637,] -0.03522990388  0.7207918            0            0 0.0072
## [638,] -0.03107616241  0.6225049            0            0 0.0076
## [639,] -0.08893925852  1.5670453            0            0 0.0100
## [640,] -0.01994238694  0.9192121            0            0 0.0064
## [641,] -0.09979141641  1.6167202            0            0 0.0104
## [642,]  0.00301192289  0.7831058            0            0 0.0056
## [643,] -0.01498796711  0.6216625            0            0 0.0044
## [644,] -0.01073756966  2.6846074            0            0 0.0048
## [645,] -0.02376932075  0.5772823            0            0 0.0060
## [646,] -0.01338174923  1.2462357            0            0 0.0080
## [647,]  0.04366993378  2.4216642            0            0 0.0060
## [648,] -0.03844091259  0.8492515            0            0 0.0092
## [649,] -0.02472460111  0.9401103            0            0 0.0060
## [650,]  0.00409398198  1.8677951            0            0 0.0064
## [651,]  0.02616464799  0.9537302            0            0 0.0068
## [652,] -0.02923016742  0.8480949            0            0 0.0052
## [653,] -0.04730909252  0.9909860            0            0 0.0096
## [654,]  0.03721849136  1.8502211            0            0 0.0072
## [655,] -0.07622043567  1.8201368            0            0 0.0080
## [656,]  0.04238053369  1.4810121            0            0 0.0064
## [657,] -0.19512873616  3.6831856            0            0 0.0104
## [658,]  0.40896904136  5.8170387            0            0 0.0112
## [659,] -0.08495184234  1.9392471            0            0 0.0084
## [660,]  0.00184211962  0.5717520            0            0 0.0044
## [661,]  0.07120549368  2.7981661            0            0 0.0040
## [662,] -0.02996484072  0.6529241            0            0 0.0084
## [663,] -0.08084038072  1.4667883            0            0 0.0080
## [664,] -0.01015284388  0.5694142            0            0 0.0080
## [665,] -0.01915263732  0.5159555            0            0 0.0072

4.3.4 Predict fitted values for each individual

pred.npb2 <- predict(fit.npb2)
fittedvals2 <- pred.npb2$fitted.vals

4.3.5 Plot predicted outcomes against “measured” outcomes

plot(fittedvals2, Y)
abline(a = 0, b = 1, col = "red")

5 Linear models for each predictor

5.1 Screening the exposures

Here I’m going to loop through some linear regression models to see if anything shows up here. Remember that the exposure and covariates have all been scaled.

The standard deviation of the mean_o3 variable is 3.06 ppb

lm_results <- data.frame()

for(i in 1:length(colnames(X.scaled))) {
  lm_df <- as.data.frame(cbind(Y, X.scaled[,i], W.scaled2))
  names(lm_df)[2] <- colnames(X.scaled)[i]
  
  ad_lm <- lm(birth_weight ~ ., data = lm_df)
  
  temp <- data.frame(exp = colnames(X.scaled)[i],
                     beta = summary(ad_lm)$coefficients[2,1],
                     beta.se = summary(ad_lm)$coefficients[2,2],
                     p.value = summary(ad_lm)$coefficients[2,4])
  temp$lcl <- temp$beta - 1.96*temp$beta.se
  temp$ucl <- temp$beta + 1.96*temp$beta.se
  lm_results <- bind_rows(lm_results, temp)
  rm(temp)
}

lm_results
write_csv(lm_results, here::here("Results", "LM_Effects_Birth_Weight.csv"))

6 Linear model with the ozone predictor

The GAM model indicates a non-linear relationship between O3 and birth weight, None of the other exposures had a PIP > 0.5. Remember that the exposure and covariates have all been scaled.

The standard deviation of the mean_o3 variable is 3.06 ppb

lm_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(lm_df)
##  [1] "birth_weight"  "V2"            "lat"           "lon"          
##  [5] "lat_lon_int"   "latina_re"     "black_re"      "other_re"     
##  [9] "ed_no_hs"      "ed_hs"         "ed_aa"         "ed_4yr"       
## [13] "low_bmi"       "ovwt_bmi"      "obese_bmi"     "concep_spring"
## [17] "concep_summer" "concep_fall"   "concep_2010"   "concep_2011"  
## [21] "concep_2012"   "concep_2013"   "maternal_age"  "any_smoker"   
## [25] "smokeSH"       "mean_cpss"     "mean_epsd"     "male"
names(lm_df)[2] <- "mean_o3"

head(lm_df)
bw_lm <- lm(birth_weight ~ mean_o3 + 
              lat + lon + lat_lon_int +
              latina_re + black_re + other_re + 
              ed_no_hs + ed_hs + ed_aa + ed_4yr + 
              low_bmi + ovwt_bmi + obese_bmi + 
              concep_spring + concep_summer + concep_fall +
              concep_2010 + concep_2011 + concep_2012 + concep_2013 +
              maternal_age + any_smoker + smokeSH + 
              mean_cpss + mean_epsd + male,
              data = lm_df)

summary(bw_lm)
## 
## Call:
## lm(formula = birth_weight ~ mean_o3 + lat + lon + lat_lon_int + 
##     latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa + 
##     ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring + 
##     concep_summer + concep_fall + concep_2010 + concep_2011 + 
##     concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH + 
##     mean_cpss + mean_epsd + male, data = lm_df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2355.51  -278.44    45.25   307.30  1337.64 
## 
## Coefficients:
##               Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)    2966.57     506.48   5.857 0.00000000667 ***
## mean_o3         -41.87      31.82  -1.316       0.18858    
## lat           -3090.26   18037.46  -0.171       0.86401    
## lon            1479.17    8493.04   0.174       0.86178    
## lat_lon_int   -3725.55   21791.93  -0.171       0.86429    
## latina_re      -106.33      48.46  -2.194       0.02849 *  
## black_re       -298.56      52.30  -5.709 0.00000001560 ***
## other_re       -105.34      70.18  -1.501       0.13369    
## ed_no_hs        167.39      78.82   2.124       0.03397 *  
## ed_hs           128.99      70.33   1.834       0.06698 .  
## ed_aa            74.00      62.00   1.194       0.23298    
## ed_4yr           77.21      52.15   1.481       0.13905    
## low_bmi        -107.61      94.73  -1.136       0.25630    
## ovwt_bmi         35.21      41.25   0.853       0.39363    
## obese_bmi       103.17      46.54   2.217       0.02691 *  
## concep_spring   -68.36      51.10  -1.338       0.18131    
## concep_summer   -26.46      76.79  -0.345       0.73048    
## concep_fall     -19.88      72.03  -0.276       0.78266    
## concep_2010     208.72     507.45   0.411       0.68095    
## concep_2011     196.49     508.25   0.387       0.69915    
## concep_2012     167.27     509.07   0.329       0.74255    
## concep_2013     256.08     507.38   0.505       0.61388    
## maternal_age     66.63      22.54   2.957       0.00320 ** 
## any_smoker     -132.39      65.27  -2.028       0.04284 *  
## smokeSH        -108.28      45.47  -2.382       0.01745 *  
## mean_cpss        12.63      20.24   0.624       0.53282    
## mean_epsd       -53.22      20.58  -2.586       0.00987 ** 
## male            160.31      33.24   4.822 0.00000167727 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 492.1 on 869 degrees of freedom
## Multiple R-squared:  0.1531, Adjusted R-squared:  0.1268 
## F-statistic: 5.817 on 27 and 869 DF,  p-value: < 0.00000000000000022
plot(bw_lm)
## Warning: not plotting observations with leverage one:
##   1

7 Try a GAM with the ozone predictor

The NPB model above indicates that there might be a signal for ozone. None of the other exposures had a PIP > 0.5. Here I’ve got a GAM with a smoothing term for ozone to see about potential nonlinear effects

library(mgcv)
## Loading required package: nlme
## 
## Attaching package: 'nlme'
## The following object is masked from 'package:dplyr':
## 
##     collapse
## This is mgcv 1.8-31. For overview type 'help("mgcv-package")'.
gam_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(gam_df)
##  [1] "birth_weight"  "V2"            "lat"           "lon"          
##  [5] "lat_lon_int"   "latina_re"     "black_re"      "other_re"     
##  [9] "ed_no_hs"      "ed_hs"         "ed_aa"         "ed_4yr"       
## [13] "low_bmi"       "ovwt_bmi"      "obese_bmi"     "concep_spring"
## [17] "concep_summer" "concep_fall"   "concep_2010"   "concep_2011"  
## [21] "concep_2012"   "concep_2013"   "maternal_age"  "any_smoker"   
## [25] "smokeSH"       "mean_cpss"     "mean_epsd"     "male"
names(gam_df)[2] <- "mean_o3"

head(gam_df)
bw_gam <- gam(birth_weight ~ s(mean_o3) + 
                lat + lon + lat_lon_int +
                latina_re + black_re + other_re + 
                ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                low_bmi + ovwt_bmi + obese_bmi + 
                concep_spring + concep_summer + concep_fall +
                concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                maternal_age + any_smoker + smokeSH + 
                mean_cpss + mean_epsd + male,
              data = gam_df, method = "REML")

summary(bw_gam)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## birth_weight ~ s(mean_o3) + lat + lon + lat_lon_int + latina_re + 
##     black_re + other_re + ed_no_hs + ed_hs + ed_aa + ed_4yr + 
##     low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer + 
##     concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 + 
##     maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd + 
##     male
## 
## Parametric coefficients:
##                Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)    2860.915    484.120   5.910 0.00000000493 ***
## lat            3305.448  17276.689   0.191       0.84832    
## lon           -1550.961   8134.939  -0.191       0.84884    
## lat_lon_int    3995.184  20872.788   0.191       0.84825    
## latina_re      -111.797     46.260  -2.417       0.01587 *  
## black_re       -305.145     49.965  -6.107 0.00000000153 ***
## other_re        -80.542     67.161  -1.199       0.23077    
## ed_no_hs        152.317     75.359   2.021       0.04356 *  
## ed_hs           126.035     67.309   1.872       0.06148 .  
## ed_aa            72.102     59.201   1.218       0.22358    
## ed_4yr           82.343     49.892   1.650       0.09922 .  
## low_bmi        -114.274     90.823  -1.258       0.20865    
## ovwt_bmi         46.224     39.434   1.172       0.24144    
## obese_bmi       116.454     44.588   2.612       0.00916 ** 
## concep_spring  -110.763     53.391  -2.075       0.03832 *  
## concep_summer   -42.155     79.128  -0.533       0.59435    
## concep_fall     -23.525     73.647  -0.319       0.74948    
## concep_2010     296.927    485.690   0.611       0.54113    
## concep_2011     268.758    486.592   0.552       0.58087    
## concep_2012     303.572    487.442   0.623       0.53359    
## concep_2013     400.030    486.002   0.823       0.41068    
## maternal_age     52.121     21.593   2.414       0.01599 *  
## any_smoker     -153.447     62.528  -2.454       0.01432 *  
## smokeSH         -80.210     43.594  -1.840       0.06612 .  
## mean_cpss         8.283     19.338   0.428       0.66850    
## mean_epsd       -51.781     19.683  -2.631       0.00867 ** 
## male            165.222     31.792   5.197 0.00000025295 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df    F             p-value    
## s(mean_o3) 5.969   7.22 12.2 0.00000000000000322 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.205   Deviance explained = 23.4%
## -REML = 6648.4  Scale est. = 2.2032e+05  n = 897
jpeg(here::here("Figs", "Ozone_GAM_Birth_Weight.jpeg"))
plot(bw_gam, main = "GAM with a smoothing term for ozone",
     xlab = "Ozone (scaled)", ylab = "Change in birth weight (g)")
dev.off()
## quartz_off_screen 
##                 2

8 GAM Sensitivity Analysis

The previous GAM suggested a possible nonlinear relationship between ozone and birth weight. However, this might be the influence of abnormally high and low exposures.

Therefore, Ander suggested a sensitivity analysis where we excluded the top and bottom 2.5% of data and just use the middle 95%.

library(mgcv)

quantile(X.scaled[,"mean_o3"], probs = c(0.025, 0.975))
##      2.5%     97.5% 
## -1.703410  1.852552
q_2.5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.025))
q_97.5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.975))


gam_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(gam_df)
##  [1] "birth_weight"  "V2"            "lat"           "lon"          
##  [5] "lat_lon_int"   "latina_re"     "black_re"      "other_re"     
##  [9] "ed_no_hs"      "ed_hs"         "ed_aa"         "ed_4yr"       
## [13] "low_bmi"       "ovwt_bmi"      "obese_bmi"     "concep_spring"
## [17] "concep_summer" "concep_fall"   "concep_2010"   "concep_2011"  
## [21] "concep_2012"   "concep_2013"   "maternal_age"  "any_smoker"   
## [25] "smokeSH"       "mean_cpss"     "mean_epsd"     "male"
names(gam_df)[2] <- "mean_o3"

head(gam_df)
gam_df2 <- gam_df %>%
  filter(mean_o3 > q_2.5 & mean_o3 < q_97.5)
hist(gam_df2$mean_o3)

bw_gam2 <- gam(birth_weight ~ s(mean_o3) + 
                lat + lon + lat_lon_int +
                latina_re + black_re + other_re + 
                ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                low_bmi + ovwt_bmi + obese_bmi + 
                concep_spring + concep_summer + concep_fall +
                concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                maternal_age + any_smoker + smokeSH + 
                mean_cpss + mean_epsd + male,
              data = gam_df2, method = "REML")

summary(bw_gam2)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## birth_weight ~ s(mean_o3) + lat + lon + lat_lon_int + latina_re + 
##     black_re + other_re + ed_no_hs + ed_hs + ed_aa + ed_4yr + 
##     low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer + 
##     concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 + 
##     maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd + 
##     male
## 
## Parametric coefficients:
##               Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)    2802.17     471.71   5.940 0.00000000420 ***
## lat            8026.65   17448.88   0.460       0.64563    
## lon           -3777.43    8215.58  -0.460       0.64579    
## lat_lon_int    9706.22   21080.80   0.460       0.64533    
## latina_re      -110.38      46.43  -2.377       0.01767 *  
## black_re       -293.91      49.93  -5.887 0.00000000573 ***
## other_re        -83.29      66.77  -1.247       0.21263    
## ed_no_hs        161.21      75.14   2.146       0.03220 *  
## ed_hs           130.69      67.01   1.950       0.05148 .  
## ed_aa            95.42      58.76   1.624       0.10476    
## ed_4yr           69.48      49.67   1.399       0.16224    
## low_bmi        -137.85      89.78  -1.535       0.12507    
## ovwt_bmi         62.86      39.47   1.593       0.11162    
## obese_bmi       120.82      44.52   2.714       0.00679 ** 
## concep_spring   -98.03      52.95  -1.851       0.06449 .  
## concep_summer   -37.90      77.82  -0.487       0.62641    
## concep_fall     -11.98      72.08  -0.166       0.86804    
## concep_2010     368.19     473.13   0.778       0.43667    
## concep_2011     356.27     474.25   0.751       0.45272    
## concep_2012     369.42     475.07   0.778       0.43703    
## concep_2013     451.57     473.60   0.953       0.34062    
## maternal_age     55.20      21.46   2.573       0.01027 *  
## any_smoker     -187.21      62.04  -3.018       0.00263 ** 
## smokeSH         -60.95      43.61  -1.398       0.16258    
## mean_cpss        19.43      19.43   1.000       0.31757    
## mean_epsd       -54.42      19.71  -2.760       0.00590 ** 
## male            145.85      31.69   4.602 0.00000484264 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df     F  p-value    
## s(mean_o3) 4.003  4.977 4.962 0.000169 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.147   Deviance explained = 17.7%
## -REML = 6273.7  Scale est. = 2.0847e+05  n = 851
jpeg(here::here("Figs", "Ozone_GAM_Birth_Weight_Sensitivity_v1.jpeg"))
plot(bw_gam2, main = "GAM with a smoothing term for ozone",
     xlab = "Ozone (scaled)", ylab = "Change in birth weight (g)")
dev.off()
## quartz_off_screen 
##                 2

9 GAM Sensitivity Analysis no. 2

Going to try the middle 90% of data as well, just in case

library(mgcv)

quantile(X.scaled[,"mean_o3"], probs = c(0.05, 0.95))
##        5%       95% 
## -1.568529  1.633168
q_5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.05))
q_95 <- quantile(X.scaled[,"mean_o3"], probs = c(0.95))

gam_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(gam_df)
##  [1] "birth_weight"  "V2"            "lat"           "lon"          
##  [5] "lat_lon_int"   "latina_re"     "black_re"      "other_re"     
##  [9] "ed_no_hs"      "ed_hs"         "ed_aa"         "ed_4yr"       
## [13] "low_bmi"       "ovwt_bmi"      "obese_bmi"     "concep_spring"
## [17] "concep_summer" "concep_fall"   "concep_2010"   "concep_2011"  
## [21] "concep_2012"   "concep_2013"   "maternal_age"  "any_smoker"   
## [25] "smokeSH"       "mean_cpss"     "mean_epsd"     "male"
names(gam_df)[2] <- "mean_o3"

head(gam_df)
gam_df3 <- gam_df %>%
  filter(mean_o3 > q_5 & mean_o3 < q_95)
hist(gam_df3$mean_o3)

bw_gam3 <- gam(birth_weight ~ s(mean_o3) + 
                lat + lon + lat_lon_int +
                latina_re + black_re + other_re + 
                ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                low_bmi + ovwt_bmi + obese_bmi + 
                concep_spring + concep_summer + concep_fall +
                concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                maternal_age + any_smoker + smokeSH + 
                mean_cpss + mean_epsd + male,
              data = gam_df3, method = "REML")

summary(bw_gam3)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## birth_weight ~ s(mean_o3) + lat + lon + lat_lon_int + latina_re + 
##     black_re + other_re + ed_no_hs + ed_hs + ed_aa + ed_4yr + 
##     low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer + 
##     concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 + 
##     maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd + 
##     male
## 
## Parametric coefficients:
##               Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)    2789.77     467.39   5.969 0.00000000363 ***
## lat            6630.85   17798.05   0.373      0.709577    
## lon           -3116.35    8379.53  -0.372      0.710069    
## lat_lon_int    8016.05   21502.25   0.373      0.709398    
## latina_re       -75.66      47.40  -1.596      0.110883    
## black_re       -283.65      50.64  -5.601 0.00000002952 ***
## other_re        -77.60      67.72  -1.146      0.252221    
## ed_no_hs        151.14      76.25   1.982      0.047813 *  
## ed_hs           119.15      68.25   1.746      0.081238 .  
## ed_aa            99.06      59.91   1.653      0.098670 .  
## ed_4yr           59.19      50.50   1.172      0.241600    
## low_bmi        -189.87      90.70  -2.093      0.036641 *  
## ovwt_bmi         41.89      40.01   1.047      0.295456    
## obese_bmi       104.96      45.59   2.302      0.021599 *  
## concep_spring  -112.02      53.61  -2.090      0.036975 *  
## concep_summer   -41.70      77.81  -0.536      0.592186    
## concep_fall     -28.33      71.99  -0.393      0.694067    
## concep_2010     425.40     468.81   0.907      0.364477    
## concep_2011     417.60     470.03   0.888      0.374572    
## concep_2012     401.55     470.80   0.853      0.393970    
## concep_2013     482.86     469.32   1.029      0.303870    
## maternal_age     57.53      21.91   2.626      0.008808 ** 
## any_smoker     -207.03      62.48  -3.314      0.000963 ***
## smokeSH         -62.64      44.24  -1.416      0.157159    
## mean_cpss        16.20      19.69   0.823      0.410687    
## mean_epsd       -52.19      20.01  -2.608      0.009281 ** 
## male            133.62      32.16   4.155 0.00003613695 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df     F p-value  
## s(mean_o3) 3.266  4.085 3.263   0.011 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.144   Deviance explained = 17.5%
## -REML = 5931.9  Scale est. = 2.0415e+05  n = 807
jpeg(here::here("Figs", "Ozone_GAM_Birth_Weight_Sensitivity_v2.jpeg"))
plot(bw_gam3, main = "GAM with a smoothing term for ozone",
     xlab = "Ozone (scaled)", ylab = "Change in birth weight (g)")
dev.off()
## quartz_off_screen 
##                 2

10 GAM Sensitivity Analysis no. 3

For completeness, just the middle 75%

library(mgcv)

quantile(X.scaled[,"mean_o3"], probs = c(0.125, 0.875))
##     12.5%     87.5% 
## -1.210585  1.170781
q_12.5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.125))
q_87.5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.875))

gam_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(gam_df)
##  [1] "birth_weight"  "V2"            "lat"           "lon"          
##  [5] "lat_lon_int"   "latina_re"     "black_re"      "other_re"     
##  [9] "ed_no_hs"      "ed_hs"         "ed_aa"         "ed_4yr"       
## [13] "low_bmi"       "ovwt_bmi"      "obese_bmi"     "concep_spring"
## [17] "concep_summer" "concep_fall"   "concep_2010"   "concep_2011"  
## [21] "concep_2012"   "concep_2013"   "maternal_age"  "any_smoker"   
## [25] "smokeSH"       "mean_cpss"     "mean_epsd"     "male"
names(gam_df)[2] <- "mean_o3"

head(gam_df)
gam_df4 <- gam_df %>%
  filter(mean_o3 > q_12.5 & mean_o3 < q_87.5)
hist(gam_df4$mean_o3)

bw_gam4 <- gam(birth_weight ~ s(mean_o3) + 
                lat + lon + lat_lon_int +
                latina_re + black_re + other_re + 
                ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                low_bmi + ovwt_bmi + obese_bmi + 
                concep_spring + concep_summer + concep_fall +
                concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                maternal_age + any_smoker + smokeSH + 
                mean_cpss + mean_epsd + male,
              data = gam_df4, method = "REML")

summary(bw_gam4)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## birth_weight ~ s(mean_o3) + lat + lon + lat_lon_int + latina_re + 
##     black_re + other_re + ed_no_hs + ed_hs + ed_aa + ed_4yr + 
##     low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer + 
##     concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 + 
##     maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd + 
##     male
## 
## Parametric coefficients:
##               Estimate Std. Error t value       Pr(>|t|)    
## (Intercept)    2867.26     455.27   6.298 0.000000000559 ***
## lat            9793.27   18535.77   0.528       0.597443    
## lon           -4589.21    8727.46  -0.526       0.599184    
## lat_lon_int   11831.89   22393.58   0.528       0.597431    
## latina_re      -100.54      50.11  -2.006       0.045240 *  
## black_re       -301.84      53.69  -5.622 0.000000028087 ***
## other_re        -72.33      71.51  -1.011       0.312204    
## ed_no_hs        127.69      83.09   1.537       0.124851    
## ed_hs           142.01      72.89   1.948       0.051816 .  
## ed_aa            70.48      63.07   1.117       0.264207    
## ed_4yr           50.59      52.98   0.955       0.340011    
## low_bmi        -273.34      98.57  -2.773       0.005714 ** 
## ovwt_bmi         56.64      42.89   1.320       0.187142    
## obese_bmi       115.88      49.29   2.351       0.019028 *  
## concep_spring  -134.92      55.91  -2.413       0.016100 *  
## concep_summer   -94.96      81.22  -1.169       0.242776    
## concep_fall     -22.23      71.43  -0.311       0.755690    
## concep_2010     382.97     456.13   0.840       0.401439    
## concep_2011     425.19     457.65   0.929       0.353196    
## concep_2012     374.58     458.34   0.817       0.414081    
## concep_2013     473.94     457.23   1.037       0.300331    
## maternal_age     50.32      23.58   2.134       0.033199 *  
## any_smoker     -208.65      67.53  -3.090       0.002090 ** 
## smokeSH         -56.16      46.26  -1.214       0.225248    
## mean_cpss        12.44      22.00   0.565       0.571985    
## mean_epsd       -58.12      21.99  -2.643       0.008410 ** 
## male            125.63      34.25   3.668       0.000265 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df     F p-value
## s(mean_o3) 1.002  1.003 2.494   0.114
## 
## R-sq.(adj) =  0.146   Deviance explained =   18%
## -REML = 4882.2  Scale est. = 1.9156e+05  n = 671
jpeg(here::here("Figs", "Ozone_GAM_Birth_Weight_Sensitivity_v3.jpeg"))
plot(bw_gam4, main = "GAM with a smoothing term for ozone",
     xlab = "Ozone (scaled)", ylab = "Change in birth weight (g)")
dev.off()
## quartz_off_screen 
##                 2